Rockburn started out in amateur hockey in his hometown, playing senior hockey with the Ottawa Gunners and the Ottawa Shamrocks. He spent the 1926-27 season with the Berlin Mountaineers of the New England Hockey League. He turned pro with the Detroit Olympics in 1927 and played with them for two seasons. In 1929-30 he played with the Detroit Cougars and in 1930-31 with the renamed Falcons. In those two NHL seasons he only scored 4 goals and 1 assist so he found himself back in the minors again in 1931-32. In the NHL he played in 94 games and scored 4 goals and 2 assists.