The woman was attacked between Main Street and Cross Arthurlie Street, Barrhead, sometime between 22:00 on Friday and 22:00 on Saturday.
Police Scotland said she was not physically injured but was left very badly shaken. They have appealed for witnesses.
The suspect was described as being tall, well built and had a beard.
Det Insp Graeme McLachlan said: "This was obviously a very traumatic incident for anyone to endure and as such I urge anyone who can provide information that could assist our investigation to contact police immediately.
"Did you see this man hanging around the area over the weekend or see him following a woman into the wooded area between Main Street and Cross Arthurlie Street?"
A 57-year-old woman has been sexually assaulted in a wooded area in East Renfrewshire.