The incident happened around 1:50 a.m. on May 2 on the 3800 block of Chestnut Street in the city's University City section.
According to sources, the victim attends the University of Pennsylvania. She was taking out the trash at Hamilton Court, an off-campus apartment complex, when she was approached by a man who was armed with a knife.
The suspect, identified by police as 21-year-old Ticquarn Thomas, fled the scene after allegedly assaulting the woman.
He was arrested on Wednesday afternoon.
Authorities originally stated the incident was an attempted sexual assault, but further investigation led to charges of rape, police said on Wednesday night.
Action News reached out to UPenn about the attack but we have not heard back. The university did alert students about the incident via a UPennAlert.
While the suspect is now in custody, students say this doesn't mean they'll be letting their guard down in terms of safety.
"He's probably not the only person who has bad intentions, so unfortunately you still have to be careful," said student Allegra Greenawalt.
Students say they try and look out for one another and always walk with friends.
"I feel very fortunate that I feel safe in the city. I'm a local as well so I've been here. But I do realize that for a lot of my female friends it's important to walk them home and make sure they get home safe, it's a different experience," said Albert Johnston Ramirec.
Police say a knife was recovered at the scene.
Anyone with information about this case is asked to contact the Special Victim's Unit at 215-685-3263/64, 215-686-TIPS (8477), or call 911.