After attending Wake Forest University from 1976 to 1979, where he was a conference all star and second in all time career sacks with 15, Parker joined the Edmonton Eskimos in 1980, right in the middle of the greatest dynasty in CFL history. He played with them for 4 years, until 1983, when he moved to the BC Lions for six seasons (from 1984 to 1989) and finished his 12 year career with the Toronto Argonauts (1990 to 1991).
Though small, Parker was famed for his quick burst off the line of scrimmage. He won the CFL's Most Outstanding Defensive Player Award three times (1982, 1984, 1986) and was an all star six times. He played in five Grey Cup games, winning four championships. During 1984 season, his first with the BC Lions, he had 26.5 sacks in a single season which is still a CFL record. Parker has the fourth-highest number of regular season quarterback sacks in CFL history, with 139.5.