Stockton was drafted by the Lambton Quay Phantoms in 1953, being taken 9th in the third round and being drafted 41st overall. Stockton would spend the next 17 years with the Phantoms until being traded in 1970 to the South Zealand Pirates. After one year with South Zealand, Stockton would have a renaissance with the Canberra Bruins where he would lead the Frontier League in homers in 1972 despite injuries. Stockton would retire in 1973 with Brisbane.