Wotherspoon first came to note as a rugby player when he represented the Cambridge University team during his student years, winning a sporting blue in 1888 and 1889. Whilst still at university he was selected to represent the Scottish national team, coming into the team to face Ireland away, in the 1891 Home Nations Championship. It was a celebrated start for Wotherspoon, scoring three tries in his debut in a 14-0 victory of the Irish. This raised Wotherspoon's status within rugby: although he did not appear in the last game of the Championship against England, he was then chosen to represent the first official British Isles team to tour, travelling to South Africa in 1891.