Robson had served in the First World War with the Seaforth Highlanders; after returning home he played for local side Vale of Leithen.
In November 1921, Robson was signed by Arsenal for £5,[1] and initially was the club's third-choice goalkeeper behind Ernest Williamson and Stephen Dunn.
With little experience and his lack of height, he was never expected to be thrust into the first team, but after first Williamson and then Dunn suffered poor form, Robson made his debut for Arsenal against Bolton Wanderers on 26 December 1922.
However, after Welsh international Dan Lewis joined Arsenal in late 1924, Robson had to share goalkeeping duties with him.
After spending the rest of the season in the reserves, Robson left Arsenal in August 1926 for Bournemouth & Boscombe Athletic.