A first information report (FIR) was Tuesday registered against Nagar at the Sodala police station here, a police officer told IANS.
Nagar told the media that he sent his resignation letter to Chief Minister Ashok Gehlot's office.
"I am resigning on moral grounds and to let the investigation agency conduct a free and fair probe," he said.
Nagar refuted the allegations and said he was being framed in "a political conspiracy".
"My house was swarming with people on Sep 11, the day when the woman says she was raped. I was not alone even for a minute," said Nagar.
Nagar represents Dudu in Ajmer district in the state assembly.
A police officer said the complainant was a married woman. She had approached a court recently, and the court directed police to register the FIR.
--IANS (Posted on 19-09-2013)