Kirton was a fine skater and playmaker with a combative side that allowed him to handle the physical demands of the NHL. He played 266 games for three teams between 1979 and 1985.
Kirton played three years with the Peterborough Petes of the Ontario Major Junior Hockey League. He scored 71 points in the 1977-78 regular season then added 26 in 21 post-season games as the Petes made it to the 1978 Memorial Cup. Although the New Westminster Bruins won the championship, Kirton was named to the Memorial Cup all-star team. He also won the George Parsons Trophy as the most sportsmanlike player in the tourney. After this fine season, Kirton was selected 48th overall by the Toronto Maple Leafs at the 1978 NHL Amateur Draft.
The young pivot enjoyed a solid year with the American Hockey League (AHL)'s New Brunswick Hawks in 1978-79. In 1979-80 he made Toronto out of training camp and scored a goal in two games before being sent back down to the farm. The young forward hurt his knee in his second game with the Hawks and was out of the lineup for a number of weeks. Rather than hang his head, Kirton continued to work on his weaknesses and averaged a point per game for New Brunswick in 61 contests after regaining his health.
After playing eleven games in 1980-81, Kirton was traded to the Detroit Red Wings for veteran netminder Jim Rutherford. He responded well to the increased ice time and scored the winning goal twice in games against his former team shortly after the trade. Kirton ended up with 18 goals in 50 games that year for his new club then 42 points in 74 games in 1981-82. Kirton was traded to the Vancouver Canucks early in 1982-83 for Ivan Boldirev. He proved to be a useful checking pivot for the Canucks in parts of three seasons. Between 1985 and 1989 he played a solid two-way role for the Fredericton Express and Newmarket Saints in the AHL before retiring in 1989.