Married Shahzad Malik, 32, made contact with his victim on SingleMuslim.com and arranged to meet her for coffee in south west London.
When he arrived he announced a change of plan and instead drove her to police accommodation in nearby Brentford.
When she expressed concern his decision, he reassured her and showed her his warrant card, the Independent Police Complaints Commission disclosed.
An investigation was launched when the woman reported the incident to police last January.
Malik, from Datchet, Berkshire, who was based at Hounslow police station, was charged with rape and two sexual offences but criminal proceedings were later dropped when prosecutors offered no evidence.
Rachel Cerfontyne, spokesperson for the IPCC, said: "This was a despicable abuse of a trusted position, which left a vulnerable young woman traumatised.
"She was subjected to assault and violation by a police officer. The officer has rightly been dismissed."
She said he was not a resident at the police section house where he assaulted her and had no permission to take a member of the public into the building.
Commander Peter Spindler, of the Metropolitan Police's directorate of professional standards, said: "This officer was the subject of some very serious allegations and the misconduct hearing, having reviewed the evidence, found that the case against him was proved.
"He abused his status as a constable for his own gratification in a most appalling way. We will not tolerate this type of behaviour, and he has therefore been dismissed from the service for gross misconduct."
A CPS spokesperson said the original charges had been dropped as there was “insufficient evidence to provide a realistic prospect of conviction.”