Curtis was signed by Cardiff as an amateur, whilst serving an electrician's apprenticeship with the Cardiff City Corporation. He signed professional terms in 1926, and in his first season won an FA Cup winners medal. He was at that time, the youngest player to appear in an FA Cup final and appeared in the only non-English side to win the cup. In 1931, whilst with Birmingham, he made another trip to Wembley but returned with a loser's medal. With Birmingham refusing Curtis' release for internationals (which were played on Saturday League programme days), he gained only gained 3 full caps for Wales.

After returning to Cardiff, Curtis clashed with the management about wages, and decided to hang up his boots. City brought him out of retirement and he was used as cover for both wing positions. During the war, he was a prisoner of war at the hands of the Japanese from 1941 to 1945.

Penalties (1 - scored)
1935-36
2 May 1936 v Torquay United H, Division Three (South), scored (keeper Percy Maggs)

FA Cup winner 1926–27
FA Charity Shield winner 1927
Welsh Cup winner 1927
with Cardiff City