The FIR was registered on Friday night in south Delhi's Safdarjung police station on the basis of the woman's complaint.
In her complaint to the police, the woman said that Rawat called her to his residence in south Delhi's Green Park area on Friday and raped her.
According to sources, the woman will be taken to a magisterial court for recording of her statement.
Sources said the woman had alleged Rawat about a decade ago that he was the father of her son.
Rawat, who was a minister then, had to resign from the government in 2003 and face a CBI probe but was cleared later. He then claimed that he knew the "distressed lady" but was not the father of her child.
Rawat, 56, was one among the nine rebel Congress legislators of Uttarakhand whose shifting loyalty led to a political upheaval in the hill state recently. He later joined the Bharatiya Janata Party.
In February 2014, a woman had filed a police case against Rawat for allegedly molesting her.
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