He played in the Eastern Hockey League from 1939 to 1941 and was the league-leading scorer in 1940-41 with 67 goals and 26 assists with the Washington Eagles. That got him up to the New York Rangers of the NHL in 1941-42, where he only managed 4 assists in 11 games. Burns finished the season with the New Haven Eagles of the American Hockey League.
Burns played in 1942-43 with the senior Montreal RCAF team and then moved to the Toronto RCAF Flyers in 1943-44. After serving in the Canadian military in 1944-45, he returned to hockey as a player-coach with the St. Paul Saints in 1945-46. Burns then played another three seasons in the minor pros and retired in 1949.