Ajmer deputy superintendent of police Vaibhav Sharma said the accused, Mojinder Verma (31), was arrested after an FIR was lodged at Ganj police station by the girl's mother late yesterday night.
The CRPF jawan has been booked under IPC sections 376 (rape) and 354 (assault or criminal force to woman with intent to outrage her modesty), and relevant sections of the Protection of Children from Sexual Offences Act (POCSO).
The police officer said that they were awaiting medical reports of the girl and the accused.
The accused was produced before a court which sent him to a day's police remand.