The singer-songwriter plays the concert ahead of the release of her second album Boys Don't Cry, which is available from May 28.
Tickets for the London show go on sale this Friday, April 20 at 9am and are priced at £28.50.
Rumer's new album is preceded by a single, 'P.F. Sloan', on May 21.
"It's a song about the great writers who have been forgotten, or sidelined by a commercially-driven music industry," Rumer said of the track.
"I think 'P.F. Sloan' sums up the whole album, and I love the idea of it being on the radio in 2012."
Boys Don't Cry is a collection of songs from the '70s which were originally sung by men, including Isaac Hayes, Neil Young, Todd Rundgren, Tim Hardin and Ronnie Lane.
Rumer played her largest ever UK tour last November, ending with a show at London's Royal Albert Hall.
Listen to Rumer's new single 'P.F. Sloan' below: