Halfway through his new memoir, Al Pacino recalls a crisis that unfolded on the set of The Godfather while filming in Sicily. Pacino was shooting a wedding scene with the actor Simonetta Stefanelli, and at one point director Francis Ford Coppola asked him to speak to the local people who were forming part of the background. But none of these extras understood English, and Pacino, despite growing up in an Italian household in New York, didn’t quite speak the language of his grandparents. Later, Coppola asked the bride and the groom to dance a waltz together, but Pacino again pleaded incompetence. Towards the end of the scene, the couple were supposed to drive away in a car, but Pacino, ever the New Yorker, didn’t know how to drive. It was at this moment that Coppola ran out of patience with his male lead. “Why did I ever hire you?” he shouted at Pacino. “What can you do?”

In many ways, Coppola’s question propels Pacino all through Sonny Boy. How did a delinquent school dropout from the South Bronx end up as arguably the most persuasive actor to ever grace a movie screen? Antiheroes have rarely seemed as manic as the chainsaw-defying Tony Montana in Scarface, or looked as vulnerable wielding a rifle as the bank robber Sonny Wortzik in Dog Day Afternoon, or just voiced as many cool lines as the reluctant mafia boss Michael Corleone in the Godfather trilogy: “Never hate your enemies. It affects your judgment.” And: “If anything in this life is certain, if history has taught us anything, it is that you can kill anyone.”

But those who dismiss his golden run in the 1970s and 80s as mostly crime capers – his longtime manager Martin Bregman would sometimes brag: “You want a successful film? Put Pacino on the poster with a gun” – also forget that the only time Pacino won an Oscar was for his sensitive portrayal of a blind lieutenant colonel in Scent of a Woman, or that he has directed documentaries about the staging of Richard III and Oscar Wilde’s Salomé. There are ways in which Pacino’s legend is built on durable improvisation – someone who knew how to make it up as he went along. If you remember The Godfather, you’ll know that Michael Corleone did dance at his wedding in Sicily and, later, whisk his bride away in a car.

Sonny Boy starts with an absorbing account of a postwar childhood spent leaping over tenement rooftops and smoking cigarettes in alleys. Pacino’s parents split up before he turned two – Pacino Sr, a war veteran, later opened a restaurant in California to cash in on his son’s reputation – and he and his mother moved in with her parents, who had a small top-floor apartment in the Bronx. Going to the movies was often the only source of entertainment for little Sonny (Pacino was nicknamed after an Al Jolson song) and his overworked single mother. His grandfather worked as a plasterer and had indeed moved to New York from a Sicilian town named Corleone.

Being the child of a broken home was Pacino’s defining wound, that and his mother’s mental health struggles – she had electroshock treatment and attempted suicide when he was six, eventually dying of an overdose when he was 22. He had a neighbourhood gang of sorts, who experimented early with drugs and alcohol, but despite her difficulties, Pacino says his mother was strict and often barred him from going out to play after sundown, and consequently “parried me away from the path that led to delinquency, danger and violence”. As a teenager, Pacino liked playing baseball but he excelled at acting in school plays. These performances were persuasive enough to label him “the next Marlon Brando”.

Pacino would, of course, go on to share screen space with Brando in The Godfather, but movies were never part of the plan in his 20s – he fancied himself as a theatre actor. He did odd jobs and enrolled in acting classes – he remembers Martin Sheen as a fellow student. Soon he was performing regularly in off-Broadway productions. In his spare time, he would ride the subway to the end of the line, reading Chekhov and Balzac. Or else he’d recite Eugene O’Neill and Shakespeare aloud in deserted alleyways. At 26, he was admitted to Lee Strasberg’s famous Actors’ Studio in New York. For a while he moved to Boston to do repertory theatre.

Nothing in the latter half of the book matches up to Pacino’s vivid rendering of his hardscrabble years. What we get instead are anecdotes and career highlights Pacino has covered for decades in interviews and talkshows. Who doesn’t know at this point that Paramount Pictures was initially opposed to his casting in The Godfather? Or that drinking was a way for Pacino to deal with his stratospheric fame? Or even that his business manager was arrested in 2010 for swindling his clients? (“I had $50m and then I had nothing.”)

You get the feeling that maybe Pacino has been famous for too long. Why else would he claim that playing Tony Montana “gave me the opportunity to uncork the underclass in myself”, or indulge in silly fantasies about how his life might have turned out if he didn’t veer into film roles? (“I’d wind up marrying a seamstress and we’d have 10 kids.”) He dutifully matches the actors he has dated with his career timeline: “I was still dating Tuesday Weld when I started working on Serpico.” A few pages later, he is involved with Kathleen Quinlan: “Kathleen was my comfort during Scarface.”

What redeems these pages are the parts where Pacino reveals his single-minded commitment to his craft. When he confesses that he was happiest during the four years he spent making Looking for Richard, or exhorts younger actors to believe in the story “as if it happened to them”, you sense that Pacino is still a twentysomething wannabe theatre actor at heart, furiously practising his lines aloud in vacant lots. Why is Pacino still thriving in Hollywood at 84, while three of his closest childhood pals from the Bronx ended up dying too early from drug overdoses? Not too long ago, an old friend called Pacino “a miracle”: “I didn’t believe that, of course. But I knew what he was saying. My whole life was a moon shot.”

• Sonny Boy: A Memoir by Al Pacino is published by Cornerstone (£25). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply