In a state with a specialty in political spectacles — over about three years, a governor has resigned in disgrace and a House speaker has been convicted on 12 felony ethics charges — Mr. Moore has reasons to think he can win this time, at least in the Republican primary in March. He was repeatedly elected chief justice of Alabama (but essentially removed), and many of his most dedicated supporters maintain that he was wronged in 2017.

But Mr. Moore, 72, remains the scarce Alabama Republican of recent years who has lost a statewide election to a Democrat. His brash, insular, unapologetic and proudly religious brand of politics made him a demagogue in the eyes of many of the state’s Democrats, and even of many of its Republicans. And the accusations of sexual misconduct, which Mr. Moore denied, are certain to be a campaign issue.

While Democrats would be more confident in Mr. Jones’s prospects if Mr. Moore were the nominee, they are not dismissing the former chief justice’s chances in a general election, particularly with the presidency also on the ballot in a conservative state.

“If you think about just the data from the past cycle, he’s a few thousand votes from being a United States senator,” said Mayor Walt Maddox of Tuscaloosa, the Democratic nominee for governor last year.

Mr. Moore’s rivals in the primary include Representative Bradley Byrne, whose 2010 campaign for governor fizzled out in a bruising primary (though he did garner more support than Mr. Moore in that race), and Tommy Tuberville, the former head football coach at Auburn University. John H. Merrill, a Republican who was re-elected last year as the Alabama secretary of state, is expected to announce his decision about a Senate campaign as soon as next week.

In an interview after Mr. Moore’s announcement, Mr. Merrill, reflecting arguments that Republicans in Alabama and Washington have made repeatedly in recent weeks, pointedly said he expected Mr. Moore would lose a general election to Mr. Jones.

Asked why, Mr. Merrill replied simply: “He hasn’t beat him before.”

For his part, Mr. Moore has been on and off the national stage for decades, mostly because of his support for the public display of the Ten Commandments — a stand that contributed to his first removal from the Alabama Supreme Court — and his opposition to same-sex marriage, which played a role in what was effectively his second ouster from the court. He has also drawn attention and criticism for his views on Islam and Sept. 11, and his uncertain command of some policy issues.