During the 1970s he appeared in three episodes each of ABC's "The Love Boat" and CBS's "Medical Center." In 1984, he appeared as C.C. Capwell in 21 episodes of the NBC soap opera "Santa Barbara." He appeared in supporting roles in a number of television series, including recurring roles in "Dynasty" from 1982 to 1988 and in Tom Selleck's "Magnum, P.I.," from 1981 to 1985 as Rear Admiral Hawkes. Burke also served as a television commercial spokesman for the RadioShack electronics retailer.