Dragana Đorđević was one of four Serbian representatives on the 1936 Yugoslavian gymnastics team that competed at the 1936 Olympic Games held in Berlin and finished fourth in the team all-around event. She scored 61.20 individual points, fifth amongst her eight teammates. By then in her mid-30s, she was once again selected to compete in 1948, where the Yugslavian team finished seventh. This time, she scored 47.60 points, ranking second amongst her teammates. Đorđević worked as a physical education teacher at the First Beograd Gymnasium High School, and was also a well-known gymnastics judge and official.