“The people of Alabama are not only angry, but they’re going to act on that anger,” Mr. Moore, a former chief justice of the State Supreme Court, said in Montgomery, the Alabama capital, as he announced his bid for the Senate seat. “The people of Alabama are tired of politicians saying one thing and doing another.”

Before he made his announcement, Mr. Moore detailed his grievances against Republican officials in Washington, and he predicted that the campaign arm of Senate Republicans would run “a smear campaign” against him.

Mr. Moore’s new campaign will test his standing among the Republican voters he cultivated — many of them white, evangelical conservatives from the state’s rural counties — as he became one of Alabama’s most divisive political figures of the last 50 years. Mr. Moore’s efforts to hold public office beyond the judiciary have faltered, sometimes in Republican primaries, and many Republicans have proved allergic to his uncompromising views or, more recently, his reputation as an accused predator.

Still, in 2017, Mr. Moore came tantalizingly close to winning a Senate seat despite allegations that he had touched or made inappropriate sexual advances toward teenage girls when he was in his 30s. Weeks after the accusations became public, Mr. Moorelost to Mr. Jones by 21,924 votes in a special election. And Mr. Moore, who never conceded to Mr. Jones, the first Alabama Democrat elected to the Senate in a quarter of a century, spent month after month carping about the outcome, the influence of Washington’s most powerful Republicans and the misconduct accusations that transformed the race he had appeared poised to win.