The 24-year-old was attacked on Friday night at about midnight. Officers say the woman was walking near the train station when she was approached by a man and then attacked in a lane.
The suspect is a white Scottish man aged between 25 and 30, slim, with short dark hair. He was wearing blue jeans.
Detective Inspector Graeme McLachlan said: “This was a terrifying ordeal for the young woman.
“Our officers are currently working with her to establish exactly where the incident occurred however we understand that it was in a lane near to Central Station.
“I would appeal to anyone who was in the surrounding area to get in touch.”