The woman has also accused the foreign national of allegedly filming objectionable videos of her, police said.
According to the police, the accused is apparently of African origin and the woman had met him through a social networking site and they had been living together.
The suspect is currently on the run and a team has been formed to nab him, police said.
A case of rape has been registered at Mehrauli police station on the woman's complaint, it said.
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In her complaint the woman has told the police that the suspect befriended her around seven months back after they met on a social-networking site.
"The two exchanged their mobile numbers and began talking to each other frequently. Soon, they came closer to each other and shifted together in a rented flat in Mehrauli. The woman has accused him of raping her at different rented flats in Mehrauli in the past six months.
"The suspect recently moved to an unknown destination and severed all his contacts with the woman as she had been pressurising him for marriage," police said.
The suspect has been in India for quite some time but he never divulged the purpose of his stay here or his personal details, the officer said.