The 23-year-old was in Crow Road, Broomhill when a man threatened her, took her into a wooded area and attacked her.
Police said the woman had been left "extremely traumatised" and that it was "imperative" they caught her attacker.
She was walking near to Cross Park in the Partick area when the man pounced at around 2.15am on Monday.
He is described as Middle Eastern in appearance, about 5ft 8in tall, slim, and aged in his mid-20s.
He spoke with a Glasgow accent.
Detective Inspector Fil Capaldi said: "A young woman has been left extremely traumatised and has been subjected to a sickening attack and it's absolutely imperative we find the man responsible.
"I appeal to anyone who may have been in the area that morning.
"This would include possible passing taxi drivers, people going home after a night out or local residents, who may have seen or heard something, please get in touch with us, your information is vital in helping us trace the man responsible."
It follows the rape of a young woman in a bin shed in Glasgow shortly before Christmas.
The 26-year-old was attacked in Riverview Gardens, Tradeston, after crossing a bridge over the River Clyde from the city centre.
The suspect is around 5ft 9in tall, with a muscular physique, with short blonde hair.
The attack near the river came after police revealed they were carrying out extra patrols at the city's bridges and the riverside area during the festive season.
Anyone with any information on either incident is urged to contact CID on 0141 532 5400 or, anonymously, Crimestoppers on 0800 555 111.