Cockburn started his SANFL career with South Adelaide in 1934, having previously played for Blyth as a teenager and young man in the Stanley Football Association, where he won the A. E. Fryar Medal a record three times.

The 1935 season also saw him win a Magarey Medal for the league's best and fairest player.

[3] During World War II he was stationed in Melbourne and in 1943 was signed up by Essendon.

He played in Essendon's five point Grand Final loss to Richmond that year.

[citation needed] Cockburn's daughter, Bronte Cockburn, played basketball for Australia women's national basketball team at the 1957 World Championship held in Brazil.