The incident took place in the Harduaganj police station area last week, but the case was registered today, they said.
The victim's family took so long to register the case as the accused had allegedly threatened them with dire consequence if they did so.
The family, however, approached SSP Mohit Gupta yesterday. The SSP has ordered a probe, they said.
The accused has been identified as a student of a local engineering college.
According to the police, at the time of the alleged rape, the victim's parents were not at home.