Career
Riordan was the Australian Labor Party member for Burke in the Queensland Legislative Assembly, winning the seat in 1918. He held Burke till 1929 at which time he resigned from the seat to successfully contest the House of Representatives seat of Kennedy at the 1929 federal election. He held the seat, improving his vote at each election, till his death in 1936.
Riordan died in 1936.
His funeral was held at Street Stephan"s Cathederal, and proceeded to the Lutwyche Cemetery.