Sen. Rand Paul (R-KY) will officially be running for both the presidency and for re-election to the United States Senate. He is the only current senator running for president that will also seek re-election to that post in 2016; Marco Rubio (R-FL) will not. (Sens. Graham and Cruz are not up for reelection in 2016.)
It initially appeared as though Paul would be unable to run for both offices as Kentucky law prevents a person from appearing on a ballot twice in the same election. To circumvent this, Kentucky's Republican Party will hold its presidential caucus in March and its "normal" primary election in May.
Paul is currently averaging about two percent in national polls.