She was so traumatised by the attack in Paisley, Renfrewshire on Tuesday January 29 that she only reported the crime last week.
The rape took place between 4pm and 7pm in a lane between Lansbury Gardens and Larkin Gardens in the Shortroods area of the town.
The woman, who was wearing a fawn-coloured jacket and jeans, was walking with the man for a short time before he attacked her.
The attacker is white, aged 40-45, 5ft 8in and has a slim-to-medium build. He has black receding hair which is longer at the back, has a scar on his left cheek, a pierced ear and wore a grey jumper, or hooded top, and jeans.
Detective Inspector David Wagstaff said: "The victim has been left so traumatised by her ordeal that she only found the courage to come forward to police last week. We are ensuring that she is given the support she requires at this difficult time.
"A search of the lane has already been carried out and officers are conducting door-to-door inquiries. I appreciate that some time has passed since the crime occurred and I would ask people to think back and consider if they recognise the description, or if they can remember if they were in the area at that time, to contact police as soon as possible."
Detectives want to trace a man who shouted at the attacker who then ran off and police are appealing for anyone who has information regarding this incident or the attack itself, or who recognise the description of the rapist, to contact Paisley police on 0141 532 5900 or Crimestoppers anonymously on 0800 555 111.