Rice will speak at a lunch Monday in Greenville on behalf of the Republican senator. Tickets are $10.
Rice and Graham agree on several foreign policy goals, including protecting American interests abroad by taking actions in conflicts. Rice was Secretary of State for nearly the entire second term of former President George W. Bush.
Graham is seeking a third term. He has six challengers in June's Republican primary who all say he isn't conservative enough for South Carolina. Many of them also say Graham is too concerned with foreign policy.
Graham will also face a Democratic and a Libertarian opponent in the fall.