The cabby who unwittingly gave cops a saliva sample that linked him to the rape of an East Village woman said he had “no idea” how his DNA came to be recovered from the woman, even as he acknowledged to cops that he sometimes picks up women off the street and has sex with them.

According to statements read at his arraignment in Brooklyn yesterday, Gurmeet Singh, 40, initially told cops that he “never” had sex in the back of his taxi, but then told them that “sometimes I pick up women, call girls, off the street and have sex with them.”

Singh told investigators, “I did not rape anybody . . . I do not know how my DNA got in her vagina,” Assistant DA Wilfredo Cotto told Judge Michael Gerstein.

Cops posing as taxi inspectors offered Singh a glass of water and matched the DNA sample from the glass to a woman who woke up being raped in a taxi on May 6.