Stevens played his junior hockey with the Kitchener Rangers, the same team as his brother Scott, and was selected 58th overall in the 1984 NHL Entry Draft by the Vancouver Canucks. While still playing in Kitchener in 1984–85, he received a surprise six-game callup to the Canucks, recording three assists.
Stevens played junior hockey with the Kitchener Rangers, where his brother Scott also played. He was selected by the Vancouver Canucks in the 1984 NHL Entry Draft and made a surprise appearance for the team during the 1984–85 season, contributing three assists.