The incident took place at a CRPF camp in Chiloda late last night, the police said.
A rape complaint was registered against Sanjay Ghame, police said, adding that he was booked under Section 376 (rape) of the Indian Penal Code (IPC).
The police said that he would be produced in court to seek further remand.
The girl informed her relative about the incident who then registered a complaint with the police, sources said.