In 1934, at the age of 19, Antal Szendey started rowing for Pannónia with his schoolmate Imre Kapossy. From 1945 to 1948, he was a competitor of the Duna EE, and from 1949 of Vasas SC. Szendey was a twelve-time Hungarian champion in different disciplines. He was a member of the national team from 1935 to 1948. With the Hungarian coxed eights, he was European champion in 1935, fifth at the 1936 Berlin Olympics, and second at the European championship in 1938. In 1937 finished third with the coxed four at the 1937 European Championships.
His rowing career was interrupted by the war. He was a reserve officer in a unit with Imre Kapossy from 1939, then in 1945 he was taken prisoner of war by France. He did not return until the summer of 1946. In 1947, along with Béla Zsitnik and non-Olympian Szaniszló Latinovits, he won the European Championship in the coxed pairs. At the 1948 London Olympics, with Zsitnik and coxswain [Róbert Zimonyi], he finished third, winning the first Olympic medal for Hungarian rowing. After his sports career he worked as a coach for Elektromos, Budapesti Honvéd and Rába ETO.