Bancroft was born Anna Maria Louisa Italiano in The Bronx, New York, the daughter of Mildred (nee DiNapoli; 1907,2010), a telephone operator, and Michael Italiano (1905 ,2001), a dress pattern maker. Her parents were both children of Italian immigrants. Bancroft graduated from Christopher Columbus High School in the Bronx in 1948.
She made her film debut in Don't Bother to Knock (1952) and, following a string of supporting film roles during the 1950s, won an Academy Award for Best Actress for her performance in The Miracle Worker (1962), receiving subsequent nominations for her roles in The Pumpkin Eater (1964), The Graduate (1967), The Turning Point (1977), and Agnes of God (1985). Bancroft's other acclaimed movies as a lead actress include Young Winston (1972), The Prisoner of Second Avenue (1975), To Be or Not to Be (1983), and 84 Charing Cross Road (1987).

Later in her career, she made the transition back to supporting roles in theatrical films such as Point of No Return (1993), Home for the Holidays (1995), Great Expectations (1998), Antz (1998),Keeping the Faith (2000), and Heartbreakers (2001). She also starred in seven television films, the last of which was The Roman Spring of Mrs. Stone (2003) for which she received Emmy and Screen Actors Guild Award nominations.