Imre Rajczy started fencing at the age of 15. From 1929-40, when he moved to Budapest, he was a fencer for BEAC. He competed in both sabre and foil but achieved his international results in sabre. Between 1933-39 he was a member of the Hungarian national team, winning the 1934 European Championship in team sabre. In 1935, he won the World University Championship both individually and in team. In the same year, he finished first at the European Championship in team and was second individually. He won gold at the 1936 Berlin Olympics as a member of the Hungarian sabre team. In 1937 Rajczy won the Golden Sabre competition in San Remo, Italy, won the Hungarian and World individual and team sabre titles, and topped the world rankings for the year.
Rajczy studied law at the Pázmány Péter University in Budapest and received his doctorate in 1935. From 1935 he was secretary-general of the Hungarian National Student Association and the editor and publisher of the University and Youth newspaper. From 1941 he was the secretary-general of the National Center of the Hungarian University and College Sports Associations and worked as a secretary at the Hungarian NOC. From 1936 he became assistant secretary in the Ministry of Religion and Public Education, and from 1943 he became ministerial secretary.
From 1945 Rajczy lived in Argentina with his family. He was the national coach of the Argentine fencing team for 10 years. From 1955 he was secretary-general of the Argentine Olympic Committee and was present at the Melbourne Olympics as a member of the official delegation. He was the chief organizer of the 1961 World Fencing Championships in Buenos Aires. From 1956-66, Rajczy was the commercial director of a vehicle manufacturer and trading company.