Rawson played football at Westminster between 1869 and 1871, becoming captain in his final year. After he was commissioned in the Army, he joined the Royal Engineers football club, and was a member of the side who reached the 1874 FA Cup Final, losing 2–0 to Oxford University. His brother William played for the opposition. The following year, the Engineers again reached the final, this time defeating the Old Etonians 2–0 in a replay, after a 1–1 draw in the first match.