In 1959 Ion Cosma won the Tour of Romania to earn himself a place on the Olympic team for the 1960 Roma Games. Cosma narrowly missed out on a medal at the Games when he came fifth in the individual road race in a group of riders who were 20 seconds behind the race winner. He also placed sixth with his compatriots in the 100 kilometres team time trial. Cosma continued to be consistent, winning another edition of the Tour of Romania in 1961 along with a stage of the Peace Race in the same year. During the mid-1960s he rode in several more editions of the Peace Race, in addition to winning the Cupa UCECOM stage race in 1963. The following year Cosma returned to the Olympics once again, competing in the individual road race and the 100 kilometres team time trial.