She started for the SC Dynamo Klingenthal and internationally for the GDR . Unger participated in the Olympic Games 1968 in Grenoble and 1972 in Sapporo part. At the 1970 World Championships in Strebske Pleso, she won the silver medal in the 3 × 5 km relay together with Gabriele Haupt and Renate Fischer . That was the first medal in Nordic skiing among women for the GDR. At the 1968 Olympics, she finished 16th over 5 km and 22nd over 10 km. 4 years later in Sapporo she reached 28th place over 5 km, 20th place over 10 km and 5th place with the relay. In 1970 she won the Svenska Skidspelenover 10 km and together with Gabriele Haupt and Karin Scheidel in the relay.
At GDR championships, she won three gold medals and four individual titles. From 1966 to 1970 she won a medal in every championship over 10 km, in the relay even from 1965 to 1973 (in 1972 no championship was held in the relay), where she won the last relay medal with the SC tractor Oberwiesenthal .
Anna Unger is married to the cross-country skier Helmut Unger , who also took part in the 1968 Winter Olympics in Grenoble.