No, he can't.
Governors fill Senate vacancies. All House vacancies are filled by special election only (but the seats are often left vacant until the next election, because special elections are a lot of trouble and cost the State money).
Thanks for the correction. Gaetz is from the dark red Pensacola area in FL so he would have no problem in a special election or in a 2022 election. He could use the time off to do book signings for his new book “Firebrand”.
“...(but the seats are often left vacant until the next election, because special elections are a lot of trouble and cost the State money).”
Have you looked at which party controls FL? Seriously?
There would be a special election in a heartbeat and no one would beat Gaetz.
He may just want to wait for the Senate run against GOPe Rino bubblebath boy Rubio.