McKenzie was born in Glasgow and trained as an upholsterer, playing amateur football for various clubs in the northern half of the city before moving to England in September 1896 to join Burton Swifts of the Football League Second Division.
At Burton he had a successful season, missing only four league matches, scoring five goals, as the Swifts finished the 1896-1897 season in eleventh place.
He then returned to Glasgow to spend a season with Clyde, at the end of which they finished at the foot of the table. In the summer of 1898, he was persuaded to move to southern England to join the Southern League champions. The "Saints" were about to embark on their first season in their new stadium and McKenzie made his debut for in the opening match at The Dell, against Brighton United on 3 September 1898.
After Watty Keay had opened the scoring, McKenzie (playing at outside-left) missed some good chances as the Saints put pressure on the Brighton goal.
As half-time approached, McKenzie made a "smart run up the left" and crossed for Abe Hartley to score the second goal. McKenzie then added a third in the second half, and although Brighton pulled one back through Roddy McLeod, Tom Smith wrapped the match up with the fourth goal.
The appreciative Saints fans dubbed McKenzie "little Joe Turner", but after only six appearances the lightweight, diminutive winger lost his place to George Seeley, and returned to Scotland.
