Long before the murder, the girls and a role in “The Godfather,” Gianni Russo was a 13-year-old with a bum arm. Freshly sprung from Bellevue’s polio ward, he ditched his neglectful parents to sleep on flour sacks in the back of a Little Italy bakery and sell pens in front of the Waldorf-Astoria.

It was 1956 and one of his regular customers was mob boss Frank Costello. The don would throw Russo a fiver and rub the boy’s withered shoulder for luck.

After a few months of that, Russo objected to being touched. Costello respected the kid’s gumption — and was even more impressed when he found out that Gianni’s great-uncle was Angelo Russo, a Sicilian kingpin who had been hanged by the Italian government in 1947 after having played a role in establishing New York’s five crime families.

As chronicled in Russo’s new memoir, “Hollywood Godfather” (St. Martin’s Press), out March 12, Costello quickly had Russo delivering packages of cash throughout Manhattan and then across the United States. Costello put up his young charge in one of a dozen apartments he kept around the city. Russo never left and continues to reside gratis in the five-bedroom Upper East Side spread.

“I’ve always had an angel on my shoulder,” Russo, now 76, told The Post over lunch at Patsy’s in Midtown. “I still carry the St. Anthony medal that my grandmother pinned to my diaper.”

Russo has enjoyed a life that is part Scorsese feature, part manifest destiny and part skin flick. He claims he had threesomes with Liza Minnelli after both took a liking to the same Vegas showgirl, and recalls scrapes with Frank Sinatra. (“He tried to slap me; I grabbed his skinny wrist and said, ‘I’ll rip off your arm and shove it up your ­f–king ass.’ ”). Once, while watching a western with Elvis Presley, Russo took cover as the King mimicked the on-screen pistol play with real guns. Less dangerous was his weird date with Zsa Zsa Gabor; the night ended with her setting him up for sex with a blonde who, “on a scale of 1 to 10, was a 12.”

Then there are the two killings he owns up to, but was never arrested for. One alleged victim was an associate of Colombian kingpin Pablo Escobar.

“Escobar wanted to murder my family in retribution; so I got John Gotti to set me up to meet with him in Colombia,” said Russo, acknowledging that he expected to take a beating or face death to save his family.

“Escobar’s guys tied me to a chair and roughed me up. Then Escobar walked in, carrying ‘The Making of the Godfather’ book. He said, ‘Why didn’t you tell me you played Carlo Rizzi?’ … He let me go in exchange for me re-enacting one of my scenes, with him playing Michael Corleone.”

(The Clark County, Nevada, prosecutor ruled the killing a justifiable homicide, and Russo, who was not charged, said it was in self-defense. He claimed that, as a pre-teen, he also murdered a man who was preying on children, but Russo said he was never charged. There is no known documentation of this.)

Russo added, “My life would make a great movie, but it is wilder than what anybody’s seen on screen.”

For instance: “Marilyn [Monroe] was the best lover,” Russo recalled. “She just wanted to please you.”

He was 16, Russo said, when he struck up an affair with the actress, then 33. Costello had asked him to keep an eye on her for the mob, which stashed its favorite moll in New York City while settling an issue she had with producer Darryl Zanuck on the West Coast. Monroe and Russo saw one another, on and off, for four years.

He claims to know how she really died. Russo showed The Post a photo of himself and the actress in 1962, at the CalNeva Lodge, a resort on the California-Nevada border. “It was taken three days before she was found dead in Los Angeles of what coroners deemed to be a drug overdose,” Russo said. The man behind the camera: Chicago crime boss Sam Giancana.

According to Russo, key members of the mob had convened at CalNeva in hopes of setting a trap for President John F. Kennedy and his brother Robert, then the US attorney general.

“They wanted to film the Kennedys in a threesome with Marilyn,” said Russo, adding that the mob anticipated using the footage to blackmail JFK into invading Cuba and returning the island’s casinos to organized criminals. The plan was scuttled after JFK didn’t show.

As Russo tells it, Monroe had fallen in with the mob while courting favor with JFK years before. When she learned of the aborted CalNeva scheme, she threatened to go to the media and basically wrote her death sentence.

“A guy known as The Doctor — a killer for hire and an actual MD; he had done major hits for the mob — injected air into the vein near Marilyn’s pubic region,” Russo said. “She died of an embolism, but it looked like drugs to the coroner.”

Still, he insisted, it wasn’t the mob that killed Monroe but, rather, the younger Kennedy, who feared the story of his and JFK’s involvement with Monroe going public.

“It had to be Bobby,” said Russo. “No one else would kill her. The mob would not have done it. They liked her. She was that party girl. Give her a couple pills, a couple drinks and she’ll f–k everyone.”

No stranger to presidential partying, Russo also recalls his own high times with JFK. “When they opened the Copa Room at the Sands Hotel [a mob-run casino in Vegas], Jack Entratter [who managed the Copacabana in New York] came out to run it and a house was built for him on the hotel’s grounds,” said Russo, adding that the president would cut loose there. “Normally, [JFK] wore a 20- or 30-pound metal brace [and suffered from severe back pain] but said he felt good when he did coke. I felt like telling him, ‘Everybody feels good, a–hole.’ He loved doing lines off of [dancer] Juliet Prowse’s stomach.”

Russo made a good living as a utility player for the mob — monitoring Vegas cash skims and laundering millions through the Catholic Church’s bank in Vatican City.

When Russo landed his role in “The Godfather,” it did not happen via normal channels. After director Francis Ford Coppola announced his plan to turn Mario Puzo’s novel into a movie, there was pushback from the American-Italian Anti-Defamation League. The group, overseen by Brooklyn mobster Joe Colombo, worried about the 1972 movie making Italians look bad. Threats were made that film unions in New York City, where the movie film was to be shot, would not cooperate with the production.

Looking to leverage the discord, Russo showed up at Paramount’s New York headquarters and strongarmed his way into brokering a deal between Colombo and studio brass. After reading the movie’s script, Colombo agreed to sanction “The Godfather” in exchange for Paramount allowing the Anti-Defamation League to put on a for-profit gala in every city where the film premiered. In return, Russo claims, he was given the role of Carlo Rizzi, abusive husband to Connie Corleone. He did not arrive quietly.

“I wore Brioni suits to the read-throughs while all the other actors dressed like slobs,” said Russo. “I hired a Chinese showgirl to drive me there in a Bentley. Everybody else took station wagons.”

Unimpressed, star Marlon Brando voiced concerns that the neophyte actor would screw up his movie.

“I’d just had a party … celebrating getting [the role],” said Russo. “This guy was going to destroy it for me? It would not happen.”

According to Russo, he got in Brando’s face and menacingly told the older actor, “Who the f–k are you to try to do this to me? I’ll cut your f–king heart out, you rat motherf–ker. I’m part of this picture whether you like it or not, you c–ksucker.”

The two became friends — a relationship cemented by Russo setting up Brando with the showgirl chauffeur, who took up residence in the latter’s hotel room. The icon provided the beginner with acting lessons that contributed to Russo snagging small roles in 46 movies (including “Every Given Sunday” and “Sea Biscuit”).

They were tight enough that Russo was the first person Brando called in 1990 when tragedy unfolded at the screen legend’s Hollywood Hills mansion.

“Christian [Brando’s then-32-year-old son] had just fatally shot his sister Cheyenne’s boyfriend,” recalled Russo. “I said, ‘Don’t call the police.’ Then I phoned [lawyer] Robert Shapiro and they got Cheyenne out of the house.”

Christian served five years for the murder and Brando kept himself from being implicated.

“The shooting was done with Brando’s gun,” Russo said. “Christian had told him that Cheyenne was getting beaten up and Brando said, ‘You’re her brother. Kill the son of a bitch.’ He probably didn’t expect Christian to do it.”

Sixty-three years after his chance encounter with crime king Costello, Russo ranks among the few golden-age mobsters who aren’t dead or in jail. But he knows that whatever he does, he’ll always be known for his portrayal of a gangster onscreen.

Indeed, when the waiter at Patsy’s serves dessert on the house, Russo can’t help but quip, “‘Leave the gun, take the cannoli.’ I can’t get away from that movie.”