The number 19 overall draft pick of the Giants in the 1986 NFL draft, out of Notre Dame, Dorsey suited up for all 16 games as a rookie, but did not breach the starting squad. Nevertheless, Dorsey was credited with three playoff games following the 1986 season, and he racked up three sacks in that playoff run to the Giants' first Super Bowl Championship.
Not starting changed in his sophomore campaign in 1987, when Dorsey started in three of 12 contests, earning himself a sack in the process.
His third season as a Giant, in 1988, was his breakout campaign, when he started in all 16 regular season games, recovering two fumbles, and earning 3.5 sacks.
Injuries derailed his season in 1989, but he was back in healthy in 1990, starting and helping shore up the Giants defense which secured the team's second Super Bowl Championship following the 1990 NFL season.
The injury bug bit once again however, with arthroscopic knee surgery coming in 1991 and then a deteriorating hip revealed in 1993. That led to an early retirement by Dorsey, ending his playing career, all spent wearing number 77 for the New York Giants in the NFL.