Tasker was selected in the ninth round (226th overall) of the 1985 NFL Draft by the Houston Oilers where he played for two seasons. He was claimed off waivers by the Buffalo Bills on November 8, 1986.
Tasker was officially listed as a wide receiver, however, most of his playing time came as a gunner, on punts and kickoffs. However, after he joined the Buffalo Bills, he began to play at wide receiver more than with the Oilers.
Tasker stands just 5 feet 9 inches (1.75 m) tall and weighed 183 lbs., however, despite his lack of size, he gained a reputation as one of the league's most feared hitters, forcing numerous fumbles. Contributing to his success in breaking up kick and punt returns was his speed; he was almost always the first player to reach the return man. He was the first player to establish himself as a star almost exclusively through special teams play without being either a kicker or a returner.
Tasker is currently a color commentator for CBS football telecasts as well as play-by-play for the local broadcasts of Bills pre-season games, working alongside his former coach, Marv Levy, who also did color commentary until becoming the General Manager of the Bills in 2006. In 2007, Ray Bentley took over Levy's place as play-by-play announcer while Tasker provided color commentary. Tasker is also the spokesperson for the West Herr Auto Group. Tasker currently works with Bill Macatee during the regular season and is on the sidelines with Jim Nantz, Phil Simms, and during the playoffs. He also worked with Don Criqui (Criqui, himself a Buffalo native, and Tasker were assigned to the majority of Bills games from 1999 to 2004) and was best known working with Gus Johnson until Johnson left for FOX Sports. He and Johnson called the David Garrard game winning Hail Mary touchdown pass for the Jacksonville Jaguars' win over the Houston Texans in 2010.
On September 9, 2007, Tasker became the 24th person inducted to the Bills Wall of Fame.
ESPNsportscasterChris Berman gave Tasker one of his famous nicknames: Steve "A-Tisker, A" Tasker. Tasker was ejected from his final NFL game, a loss to the Green Bay Packers in 1997, for bumping a referee.