Rezső Wanié was a swimmer and water polo player of KISOK (National Circle of Middle School Athletes), and from 1929 of the Szegedi Úszó Egylet.
He had his biggest successes together with his younger brother András.
They won together a bronze medal at the 1927 European Championships in Bologna as a member of the 4 × 200 freestyle relay and were fourth in the same discipline at the 1928 Olympics. He also competed in the 400 and the 100-meter freestyle. He was eliminated in the second qualifying round.
Rezső did not compete after the Olympics.
Following World War II, Rezső and his family emigrated to Canada, then moved to the United States and settled in Sacramento.