Police said the 42-year-old was left so traumatised by the attack that it she has only just "found the courage" to report it.
It happened in Shortroods, Paisley, on Tuesday, January 29.
Officers said the woman had been walking with the man before he raped her in a lane between Lansbury Gardens and Larkin Gardens. It happened between 4-7pm.
Detective Inspector David Wagstaff said: "The victim has been left so traumatised by her ordeal she only found the courage to come forward to police last week.
"We are ensuring she is given the support she requires.
"I am appealing for anyone who may have been in the area between 4-7pm on that date to contact us.
"In particular, I am keen to trace a man who shouted at the attacker because this appeared to disturb him and he ran off."
Police said the rapist was 40-45 about, 5ft 8 ins and of slim-medium build, with a scar on his left cheek.
He had black receding hair, which was slightly longer at the back, had a pierced ear and was wearing a grey jumper or hooded top and jeans.
Mr Wagstaff added: "A search of the lane has been carried out and officers are conducting door to door inquiries.
"I appreciate some time has passed since the crime happened 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 call us as soon as possible."
To help jog memories, police said the victim was wearing a fawn jacket and jeans at the time of the attack.
Anyone with information is asked to call Paisley police office on 0141 532 5900.