The former federal prosecutor and New York City mayor was ordered to pay a $150,000 bond and told not to attempt to intimidate any of his 18 co-defendants or witnesses in the case, according to court papers.
"This indictment is a travesty," Mr Giuliani told reporters after his appearance. "This is an assault on the Constitution."
Mr Giuliani is one of 18 co-defendants alongside Mr Trump charged by Georgia prosecutors of trying to reverse the former president's defeat in the state.
Fulton County District Attorney Fani Willis brought the charges against Mr Giuliani, Mr Trump and their co-defendants.
“I'm going to Georgia and I'm feeling very, very good about it because I feel like I'm defending the rights of all Americans,” he said in New York ahead of his trip to Georgia.
Most defendants so far have negotiated bond agreements to avoid being held in jail ahead of their arraignment hearings.
John Eastman, Mr Trump's former lawyer, and Republican poll watcher Scott Hall surrendered to the Fulton County sheriff's office on Tuesday. Booking photos of Mr Eastman and Mr Hall were released later in the day.
Former Georgia Republican Party leaders Cathy Latham and David Shafer were booked overnight.
Mr Giuliani scoffed at the idea of his mugshot being taken.
“I get photographed. Isn't that nice? A mugshot of the man who probably put the worst criminals of the 20th century in jail,” he said.
Mr Giuliani is being charged under the Racketeering Influenced and Corrupt Organisations Act, which is used to take aim at criminal organisations. It is the same law that Mr Giuliani used to go after mob bosses while he was mayor.
The former mayor was one of the most vocal supporters of Mr Trump's false election fraud claims.
Mr Trump said he would surrender to his charges on Thursday. He has already negotiated a $200,000 bond deal.