At the age of 18, Randy Bucyk enrolled at Northeastern University in 1980. For four years he was one of the school's top scorers. In his rookie season he played in 31 games, scoring 18 goals and 35 points. He followed that up with two 36-point seasons and a 29-point season in his senior year.
In 1984-85, Bucyk turned pro, signing a minor-league deal with the Montreal Canadiens. He dressed for 62 games with Montreal's farm team in Sherbrooke, and scored 21 goals and 47 points. The following year Bucyk was called up the Montreal, where he appeared in 17 games, scoring four goals and six points. It was not until 1987-88 that Bucyk got his second and last shot at the NHL, playing two games with the Calgary Flames.
Bucyk played three more years of professional hockey in the IHL with the Salt Lake City Golden Eagles and also dressed for four games with the Canadian National Team before retiring in 1991. In 19 NHL games, Bucyk had four goals and six points.