Born and educated in Milton, Bloxham represented the local Tokomairiro club, and won a place in the Otago provincial side from 1974 to 1986, playing as hooker. He captained Otago between 1980 and 1982.
He briefly represented New Zealand in 1980 when he was called on as a replacement player during that year's tour of Fiji. He played in two matches, including the international against Fiji, but the game was not given full test status by the New Zealand Rugby Union.
Bloxham died of cancer in Dunedin on 10 October 2000.