The man followed the 24-year-old into a basement area in Brunswick Street, Glasgow, and raped her after walking with her in nearby Ingram Street at around 1.25am yesterday.
Police have been scanning CCTV images and carrying out door-to-door inquiries to try and trace the attacker.
He is described as white, aged between 20 and 30, around 5ft 10in and of medium build.
He has strawberry blonde hair and was wearing a dark-coloured jumper, which was possibly blue, with a white shirt, blue jeans with an emblem on the back, right-hand side pocket, and dark shoes.
Detective Inspector Craig Willison said: "I would like to assure people that we are determined to trace the perpetrator of this crime."
He added: "This area is surrounded by bars and clubs and although it was in the early hours of the morning, I'm sure people would have been out and about. I am appealing to anyone who may have been in the vicinity to get in touch with us. You may think what you know is not significant but please do pass on any details - your information could prove vital and help us trace the man responsible.
"People mustn't feel that they have to avoid going out or enjoying themselves but be aware that there are predators who will seek out people who appear vulnerable. We have additional patrols in the area to provide reassurance to local people and anyone with concerns can raise them with these officers."
Anyone with information is asked to contact officers at the Rape Investigation Unit at London Road on the non-emergency police number 101, or Crimestoppers on 0800 555 111 where information can be given anonymously.