Roberts was a member of Memorial Cup and Minto Cup winning teams as Canadian junior hockey and box lacrosse champions, respectively. He was a first round selection of the Calgary Flames, 12th overall, at the 1984 NHL Entry Draft and played ten seasons in Calgary. Roberts was a member of the Flames' 1989 Stanley Cup championship team and made two of his three NHL All-Star Game appearances as a representative of the team. A serious neck injury forced him to miss the majority of two seasons, and while his return earned him the 1996 Bill Masterton Memorial Trophy for perseverance and dedication to the game, he was forced into retirement following the 1995–96 season.