Rainier Ehrhardt/Associated Press
Mr. Graham’s entry into the race comes a year after his political career appeared briefly to be on the ropes, when Tea Party conservatives targeted him as a moderate to be ousted in the midterm election.
After fending off that challenge with ease, Mr. Graham, 59, has said his fear that the world is “falling apart” inspired him to run for the White House. He will try to convince voters that a platform of pragmatism at home and “security through strength” abroad is the formula that gives Republicans the best chance to beat Hillary Rodham Clinton if she becomes the Democratic nominee.