Walker made his Broadway debut as the Archbishop of Canterbury in the famous 1960 production of Jean Anouilh's "Beckett," which starred Laurence Olivier and Anthony Quinn. He subsequently appeared in 22 Broadway productions from 1960 to 1973.

Walker made his movie debut in the Kirk Douglas movie A Lovely Way to Die (1968) and played the doctor in Love Story (1970). He made five appearances on the CBS Radio Mystery Theater in 1974. His last film was Getting Even with Dad (1994), but his most famous movie role came two years earlier in the film adaptation of Prelude to a Kiss (1992), in which he reprized the role of the Old Man he had assayed in the 1988 Berkeley Repertory production of the Craig Lucas play.