Lindsey Graham, a 59-year-old senator from South Carolina, says he is running for president "because the world is falling apart".
Mr Graham is one of the party's most outspoken foreign policy hawks, and advocates sending 10,000 US ground troops to Iraq and Syria to take on the Islamic State.
He is a close ally of Senator John McCain, the 2008 Republican nominee, and a critic of the Tea Party.
Mr Graham is the only candidate in the field to have never been married.