Roberts was nominated for the Academy Award for Best Supporting Actor in 1985 for his role as the escaped convict Buck in the film Runaway Train. In 1987, he won the Theatre World Award for his Broadway debut performance in Burn This.

Roberts's starring roles include King of the Gypsies (1978), Raggedy Man (1981), Star 80 (1983), The Pope of Greenwich Village (1984), The Coca-Cola Kid (1985), Rude Awakening (1988), Best of the Best (1989), By the Sword (1991),Best of the Best 2 (1993), The Specialist (1994), The Immortals (1995), La Cucaracha (1998), Purgatory (1999), and Con Games (2001). In 1996, he appeared in the Doctor Who TV movie in the role of the Master, and played the Archangel Michael in 1997's The Prophecy II. He also appears in the 2000 film Race Against Time as a father who sells his organs to pay for hospital treatment for his son and in the 2003 film Spun as "The Man" alongside Mickey Rourke and Jason Schwartzmann. He also performed the voice of Dark Danny in N