The man pounced as the victim, aged 23, was making her way home early on Hogmanay.
She was threatened by the man at around 2.15am on Monday before he dragged her into bushes at Cross Park in Partick and assaulted her.
The suspect is described as 5ft 8in and in his mid-20s and was seen running away.
He is said to be of Middle Eastern appearance and spoke with a local accent.
He is slim with short dark hair and wore a white tracksuit jacket.
Officers believe the public may hold clues.
Detective Inspector Fil Capaldi said: "This would include possible passing taxi drivers, people going home after a night out or local residents."
It follows the rape of a woman in a bin shed in Riverview Gardens, Tradeston, Glasgow just before Christmas.