Constable Ian Naude told the jury that the sex was consensual and that the girl "seemed to be enjoying it".
Naude was assigned to a unit dealing with vulnerable youngsters.
It emerged during the trial that he was named as a sexual offence suspect in neighbouring forces before joining the Cheshire Police in England's northwest.
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The court heard that the constable had visited the 13-year-old's home three days earlier to investigate a domestic violence case.
He was found guilty of picking her up off the street and raping her in the back seat.
"In order to impose your will on a young girl... you used and abused your position as a Cheshire Police officer, thereby enabling you to satisfy your lust and perversion," said judge Clement Goldstone.
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