Ravenel, 44, is also the South Carolina state treasurer, and Gov. Mark Sanford immediately suspended him after Tuesday's federal grand jury indictment, the Spartanburg (S.C.) Herald Journal reported Wednesday.
Ravenel, a millionaire in real estate, and a second man were indicted on a charge of conspiracy to possess with the intent to distribute cocaine.
Giuliani political director Mark Campbell said in a statement in the campaign Web site Ravenel had "stepped down from his volunteer responsibilities with the campaign."
Arraignment for Ravenel is set for July 9. If convicted, he could be sentenced to 20 years in prison and fined $1 million, reports said.