"I'm not here to get my name in the paper," he said. "I get that every day, anyway."
Arpaio, who has frequently talked about seeking higher office, said he decided to run as a "big supporter of President Trump" who would back the president wholeheartedly. In the primary he will face Kelli Ward, a former state senator also running as a Trump ally.
His decision may create an opening for Rep. Martha McSally, an Arizona Republican with more-moderate views on immigration who is contemplating a bid for the seat and is backed by party leaders in Washington.
"You could argue that it splits up the 'Trumpy' vote," Flake (R-Ariz.) said Tuesday, "but that assumes Kelli Ward stays in the race."
Arizona does not require runoffs in Senate elections, allowing candidates to win nominations with pluralities of the vote. Ward's allies, who were girding for a long primary against McSally, took the news in stride.
"Sheriff Joe has been a patriot, but at the end of the day in terms of running for this election, Kelli Ward is going to be hard to beat," said Eric Beach, a political strategist for Ward's campaign. "I'm confident that this will not split the vote. The reality is that Kelly has a lot of momentum in the race."
The former sheriff's decision came as a surprise to some Democrats, who thought Arpaio's career had ended in 2016. After 24 years as Maricopa County's chief law enforcement officer, Arpaio was handily defeated in the sheriff's race by Democrat Paul Penzone. Trump carried the county by three points; Arpaio ran 12 points behind Penzone, losing by more than 130,000 votes.
Eight months later, Arpaio was convicted of criminal contempt for having ignored a judge's order to stop detaining immigrants simply because he suspected that they lacked legal status. But he had an ally in President Trump, who had campaigned alongside Arpaio. Trump said the former sheriff was treated "unbelievably unfairly."
Within weeks of the conviction, Trump granted Arpaio a full and unconditional pardon — the first of his presidency. Democrats cried foul, and dozens of them filed an unsuccessful lawsuit to stop the pardon. Arpaio returned to public life, speaking at a fundraiser for a congressional challenger to Rep. Maxine Waters (D-Calif.).
Arpaio's Senate bid is making Democrats even more bullish on a race in which Rep. Kyrsten Sinema (D-Ariz.) has already consolidated most of the Democratic support. Sen. Chris Van Hollen (D-Md.), who chairs the Democrats' 2018 Senate campaign efforts, said Sinema would run on "kitchen-table issues" while Republicans run on divisiveness.
Rep. Ruben Gallego (D-Ariz.) told reporters last year of Arpaio, "We beat him like a drum in 2016, and we'll beat him like a drum if he runs again."
Asked Tuesday about Arpaio's decision, Gallego amended his prediction: Democrats would beat Arpaio "like a drum at a college football game," he said.
Sen. Cory Gardner (R-Colo.), who leads the GOP's efforts to expand its majority in 2018, rejected a reporter's suggestion that Arpaio could create the same sort of challenges for the party that Roy Moore created in Alabama. "I think there's a lot of people who are going to be running, and that's that," Gardner said.
Other Democrats used the Arpaio news to encourage donors to start giving to their campaigns. Former congresswoman Ann Kirkpatrick, a Democrat now seeking McSally's Tucson-area seat, said in an email to donors that Arpaio's "hatred and intolerance have no place representing our great state." The turnout group Voto Latino sent a message to donors saying that Arpaio should in "no way, shape or form be anywhere near our government."
Flake, meanwhile, suggested that Arpaio's run looks like a scam. He said he was not sure that the former sheriff would even stay in the race.
"Write about it now, because it won't last long," Flake said. "He's talked about this so many times, and this is the furthest it's gone, but it won't last."
Michael Scherer contributed to this report.