The constable, Giriraj Singh (23), has been detained for questioning.
Singh, a resident of Ghaziabad, was posted in Samai Pur Badli area since 2013 and had befriended the girl, who is pursuing graduation from the School of Open Learning in Delhi University, a police officer said.
The girl approached Samai Pur Badli police station in Outer Delhi yesterday and filed a complaint alleging that Singh had raped her about two months ago in a hotel in the same area on promise of marriage.