The incident took place on August 3 in Kekri, a block around 135 km from the state capital, they said.
"Kanya Devi Raigar was branded a witch and severely tortured before being beaten to death, she was also made to eat faeces by her relatives," Superintendent of Police (SP) of Ajmer, Rajendra Singh, said.
The police registered a case today against four people -- Pinky Raigar, Sonia Raigar, Mahaveer Raigar and Chandra Prakash Raigar -- under relevant IPC sections, including murder, and provisions of the Rajasthan Prevention of Witch- Hunting Act, 2015.
The woman succumbed to injuries at the spot, the police said.
On claims that the relatives had pierced her eyes with a hot rod, SP Singh said the body was cremated by the relatives and no post mortem could be conducted, "so it is proving difficult to ascertain these claims".
The woman's husband died about a month ago and she was living with her son and daughter, the police said.
The police said a distant relative of the woman had lodged a complaint on August 10.
"I had received the complaint on August 10 from a relative, but we could not file an FIR as the complainant was not a close relative of the deceased," SHO at the Kekri Police Station Hari Ram Kumawat said.
However, after the woman's daughter lodged a complaint, the police registered a case, he said.