Rinnat Safin made his international début at the 1967 World Championships, where he won silver as a member of the Soviet relay team and was fourth in the 20 km. Safin was not selected to the Soviet 1968 Olympic team, but competed at the 1969 World Championships, where he won a silver at 20 km and a World title in the relay.
He would won three more World titles in the relay in 1970, 1971 and 1973, while his best individual place in those championships would be fifth in 1971. Safin also competed at the 1972 Olympic Games, where he was disappointing 19th in the individual 20 km and won gold as a member of the Soviet relay team. Domestically Safin won Soviet titles in the individual 20 km in 1971 and in the relay in 1967 and 1970-72.