Rudolph W. Giuliani turned himself in on Wednesday in the racketeering case against former President Donald J. Trump and his allies, surrendering at the Atlanta jail where the defendants are being booked.

Mr. Giuliani, whose bond was set at $150,000, arrived in Atlanta as another defendant in the sprawling case, the lawyer Kenneth Chesebro, filed a motion seeking a speedy trial. Under that scenario, which Georgia law allows, the trial for all 19 people indicted in the case would have to start no later than Nov. 3, months earlier than prosecutors had sought.

After his booking, Mr. Giuliani, the former mayor of New York, stepped out of an S.U.V. to address a throng of reporters, calling the case “an attack on the American people.” He then made his way to A 2nd Chance Bail Bonds, a business near the jail.

He and Mr. Trump face the most charges among those indicted in the case. Mr. Giuliani served as Mr. Trump’s personal lawyer in the aftermath of the 2020 election and played a leading role in advancing false claims that the election had been stolen from Mr. Trump.

Bernard Kerik, who served as New York City’s police commissioner during Mr. Giuliani’s tenure as mayor, accompanied him to the jail in Atlanta. Mr. Kerik is not a defendant in the case. Also traveling with Mr. Giuliani, who flew to Atlanta on a private plane, were Ted Goodman, a spokesman for Mr. Giuliani, and John Esposito from the New York law firm Aidala, Bertuna and Kamins. Mr. Esposito is expected to take the lead in representing Mr. Giuliani, someone familiar with the arrangement said.

The former mayor’s lawyers met with the office of Fani T. Willis, the Fulton County district attorney who is leading the investigation, ahead of his booking.

Bond for another defendant, Sidney Powell, a lawyer who advanced false claims of vote fraud and advised Mr. Trump to fight his election loss, was set on Wednesday at $100,000.

The bond for Mr. Trump, who plans to turn himself in on Thursday, has been set at $200,000; it includes stipulations that he not intimidate witnesses or co-defendants, whether in social media posts or otherwise.

The case against Mr. Giuliani is a striking chapter in the recent annals of criminal justice. A former federal prosecutor who made a name for himself with racketeering cases, he now faces a racketeering charge himself.

“This is a ridiculous application of the racketeering statute,” he said last week after the indictment was issued.

Nearly half of the defendants in the case have already made the trip to the Fulton County jail to be fingerprinted and have mug shots taken. They include Mr. Chesebro and John Eastman, the two architects of the plan to use fake electors to keep Mr. Trump in power after he lost the election to Joseph R. Biden Jr.

David Shafer, a former chairman of the Republican Party in Georgia, has also turned himself in, as has Scott Hall, a pro-Trump Atlanta bail bondsman who was involved in a data breach at a rural Georgia elections office.

In a social media post on Wednesday, Mr. Trump — who is running for office again, leads the Republican presidential primary field and is skipping his party’s first debate on Wednesday night — sounded a defiant note about his upcoming visit to the Atlanta jail, saying he would “proudly be arrested” Thursday afternoon.

Mr. Giuliani has struggled financially with mounting legal expenses, many of them related to his efforts to keep Mr. Trump in office for another term after the 2020 defeat. After repeated entreaties from people close to Mr. Giuliani, Mr. Trump plans to host a $100,000-per-person fund-raiser next month at his club in Bedminster, N.J., to aid the former mayor, according to a copy of the invitation.

While Mr. Trump’s traditional strategy throughout his many legal entanglements has been to slow things down, Mr. Chesebro’s filing for a speedy trial was the latest twist in the Atlanta case. Speedy trial demands are not unusual in Georgia. Ms. Willis’s office has been prepared for the possibility of a defendant requesting one, and it factored into her office’s decision to take its time in bringing an indictment after a two-and-a-half-year investigation.

“State law, if requested by a defendant, sets a firm time limit in which to have a fair trial,” Mr. Chesebro’s lawyers, Scott Grubman and Manny Arora, said in a statement. “Mr. Chesebro has given his official notice that he intends to avail himself of that right. Mr. Chesebro maintains his innocence and remains confident as the legal process continues.”

A speedy trial would apply to all 19 people indicted in the case. But some defendants are seeking to move their case to federal court or have said they will seek to sever their case from the other defendants’, so the ultimate timing of a trial or trials remains up in the air.

The three defendants who have filed to remove their case to federal court are Jeffrey Clark, a former Justice Department official; Mark Meadows, Mr. Trump’s former White House chief of staff; and Mr. Shafer.

Robert G. Rubin, a veteran Atlanta-area defense lawyer, said defendants had a statutory right in Georgia to a speedy trial.

“It’s not something that the judge gets to grant and not grant,” he said. “If you file it in time, then you have that right. And it affects not only you but your co-defendants as well, because they’re under the same ticking clock once one defendant files it.”

Defense lawyers often file speedy trial demands if their client is waiting in jail without a bond. In other cases, it can be a tactical maneuver to force prosecutors to go to trial before they are ready. But in this case, Mr. Chesebro is out on a $100,000 bond. And Ms. Willis has had more than two-and-a-half years to prepare her case.

Mr. Rubin said he respected the skills of Mr. Chesebro’s lawyers. “But I don’t know what the advantage is for Mr. Chesebro,” he said.

Mr. Clark and Mr. Meadows also filed court papers seeking to block their arrest. On Wednesday, the federal judge handling the matter, Steve C. Jones, rejected their arguments and said the case would proceed while he weighed the removal question.

Ms. Willis’s office, in its own filing, called Mr. Meadows’s bid to remove the case to federal court “meritless.”

Norman Eisen, a special counsel to the House Judiciary Committee during the first impeachment of Mr. Trump in 2020, said he doubted that the removal attempt would be successful.

“Removal is only for official business and what they did was way outside the bounds of anything official,” he said, adding that Judge Jones had “already ordered a brisk briefing and hearing schedule. That’s an indicator that he’s going to bring things to a head, and quickly.”

Shane Goldmacher and Sean Keenan contributed reporting.