The alleged attack reportedly occurred inside the LaGuardia House on January 18 around 7:30 a.m.
The 19-year-old victim was followed into the apartment building and then into the elevator, where the suspected pulled out a knife and forced the woman out of the elevator and into the stairwell to sodomize her, police said.
According to police, the suspect took pictures of the victim with a camera phone before fleeing the scene.
The suspect is described as Hispanic male with a dark complexion, between the ages of 18 to 23 years old. He is between 5'8" to 5'10" and weighs about 200 pounds. He has a medium build and a black Afro.
He was last spotted wearing a black North Face jacket, blue jeans and black boots.
Anyone with information is urged to contact Crime Stoppers at 1-800-577-TIPS (8477).