Born in Pittsburgh, Pennsylvania of Italian/Syrian heritage, Abraham attended the University of Texas, then studied acting under Uta Hagen in New York. He began his acting career on the stage, making his stage debut in a Los Angeles staging of Ray Bradbury's The Wonderful Ice Cream Suit.
Although his filmography is not large, he has always turned in competent performances. He won the Academy Award for Best Actor for Amadeus, and has appeared in such other films as The Big Fix, Scarface, The Ritz, The Name of the Rose, An Innocent Man, The Bonfire of the Vanities, Last Action Hero and Star Trek: Insurrection.