Tanner was educated at Gowerton Grammar School, and was still a schoolboy when he played at scrum-half for Swansea against the All Blacks at St. Helens in 1935. Swansea won the game by 11 points to 3, with Tanner and his cousin Willie Davies outstanding. The New Zealand captain, Jack Manchester, is said to have passed back the message to New Zealand: "Tell them we have been beaten, but don't tell them it was by a pair of schoolboys".
In December the same year Tanner won his first cap for Wales at the age of 18 years and 11 months, making him one of the youngest players to appear for Wales. The match was again against the All Blacks, and Tanner was again on the winning side. He went on to win 25 international caps, 12 as captain, despite his career being interrupted by the Second World War. His last international match was against France in 1949.
Tanner toured South Africa with the British and Irish Lions in 1938 and played in one test.