The most vulnerable Democratic senator heading into next year’s midterm election has drawn his first challenger.

Representative Buddy Carter of Georgia, a Republican, announced his entry on Thursday into the primary race seeking to challenge Senator Jon Ossoff, just days after Gov. Brian Kemp took himself out of contention.

Georgia Republicans had been waiting for months to see whether Mr. Kemp would run for the seat. He would have instantly been seen as a front-runner and a formidable challenger to Mr. Ossoff, a first-term senator.

Mr. Carter, the first Republican to take advantage of the opening, would be a relatively mainstream option, but the field could grow crowded.

Republicans in the state have worried in particular that Representative Marjorie Taylor Greene, the polarizing Trump ally who has said she is considering running, could win a primary race by attracting the most fervent right-wing voters only to lose in the general election by turning off independents and disaffected, more centrist Republicans.

Ms. Greene said in a television interview this week that she was considering a run either for Senate or for governor in 2026, and that polling showed she could win either primary. “That’s a choice that I can make, and I’ll give it some thought,” she said.