Short for role play. Typically for games.
But nowadays teenagers "RP" someone so they take some random persons face from Tumblr or instagram and pretend to be that person.
*girl walks bye*
Rich: dammmnn girrl clean that RP of yours...I'm dyin over here
Jen: RP whachu talkin bout?
Rich: Rank Pussy Jen that's you....RP.
Jen: uhhhh