Clifford Atherton Riordan was born on 24 December 1885. He attended SACS and played provincial rugby for Transvaal on test debut.

"Cliff" was the son of Hussey de Burgh Twiss Riordan, SV/Prog and Caroline Alice Frances Riordan. He was married to Mabel Kemmish and they had a daughter, Mabel Riordan. Riordan played in the first two test matches of the 1910 series against Britain. The first test took place at the Wanderers Stadium in Johannesburg with Dougie Morkel captaining a Springbok side who had nine debutants, including Riordan. South Africa won the match 14-10, outscoring the British by four tries to two. His second (and last) test was played in Port Elizabeth at the Crusaders ground in front of a crowd of seven thousand spectators. Billy Millar took over the captaincy from Dougie Morkel. The British won the game 3-8, scoring two tries to South Africa's one. South Africa's only try was scored by debutant Wally Mills who played on the left wing. Riordan was dropped for the last test where South Africa went on to win emphaticly at Newlands to secure a series win.

Cliff Riordan died on 7 February 1958, aged 72.