Árpád Domján began his athletic career as a footballer, but before long switched to water polo. Domestically, he joined the Ferencváros team, while internationally he started represented Hungary beginning in 1955. He was not, however, selected to represent his country in the tournament at the 1956 Melbourne Olympics, but was given a non-starting spot in the 1500 metres freestyle swimming event so that he could attend the Games with his partner Katalin Szőke. The duo did not return to Hungary after the Olympics and eventually settled in Los Angeles, marrying in 1961. By career he worked as an architect, later running his own company.