Born Annegret Irrgang, she won her first international title at the 1971 European Championships, as a part of her country's 4 x 100 m relay team. The next year, at the 1972 Summer Olympics in Munich, she finished 5th in the 100 m, in front of her home crowd. As she had married hurdler Manfred Richter, she now ran under that name. With the relay team, Richter ran a new World Record, beating rivals East Germany for the gold.
Before the 1976 Summer Olympics, everybody's attention was not directed at Richter, but at fellow Dortmunder Ingeborg Helten, who had set a new World Record of 11.04 just prior to the Games. Richter was beaten in heats by the defending champion Renate Stecher of East Germany, but Richter ran 11.05 in the second round and set a world record of 11.01 in the semifinals. In the final, Richter and Stecher finished within one metre of each other, with Richter winning the gold and vanquishing Stecher. Three days later she won a silver medal in the 200 m and another one in the 4 x 100 m relay, being beaten by East Germany this time.
Richter retired the next year, but made a short comeback in 1978, which ended with a severe injury.