PC Michael Graham, 47, an officer in Hounslow, has also been charged with assault.
The offences are alleged to have taken place between 24 December 2013 and 2 September 2014 while the officer was off duty.
He was arrested on 6 October and is due to appear at Uxbridge Magistrates' Court on 21 October.
The Directorate of Professional Standards has been informed, Scotland Yard said.
A Met Police officer has been charged with seven counts of rape.