The police received a call from the woman around 3.15 a.m. Tuesday from Hauz Rani area in south Delhi, where the 23-year-old accused lives.
Police said the woman was accompanied by a female friend, and both were in an inebriated state.
Both were taken to the Malviya Nagar police station in south Delhi.
Police added that on the basis of their allegation, they have registered a rape case and taken the accused into police custody.
The accused Afghan youth was known to the girls.