CENTRAL, S.C. — Senator Lindsey Graham of South Carolina returned Monday to the neighborhood where he was raised to announce that he is running for president, injecting a hawkish foreign policy voice into a crowded field of Republican contenders.

Mr. Graham entered the race a year after his political career appeared briefly to be on the ropes, when Tea Party conservatives portrayed him as a moderate and tried to force him out of the Senate.

After fending off that challenge with ease, Mr. Graham, 59, has said his fear that the world is “exploding in terror and violence” 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 to give Republicans the best chance to beat Hillary Rodham Clinton if she becomes the Democratic nominee.