No, Trump cannot win Georgia’s electoral votes through a write-in Senate campaign.

President-elect Joseph R. Biden Jr. won Georgia, but that has not stopped people from claiming that President Trump still has a chance to change the outcome and win the state’s 16 electoral votes.

The hashtag #WriteInTrumpForGA was one of Twitter’s top trending topics on Tuesday afternoon, with more than 23,000 tweets. Many called for Georgia voters to cast their ballots in January’s runoff elections for the state’s two Senate races for Mr. Trump. Doing so, the tweets claimed, would change the election results and get Mr. Trump re-elected.

That isn’t true. Georgia officials certified Mr. Biden’s victory in the state last week, and Senate races have no bearing on the presidential election. Furthermore, runoff elections in Georgia do not permit write-in candidates. In fact, state officials said, there is no line allocated for a write-in on the paper ballot or a button for it on touch-screen voting.

“Our voters are definitely going through some kind of emotional abuse right now,” Jordan Fuchs, Georgia’s deputy secretary of state, said in an interview. “There’s not even an option to write in a candidate.”

Georgia on Tuesday began a machine recount of the votes cast in the presidential election after a request from Mr. Trump’s campaign, which was allowed under state law because the margin was less than 0.5 percentage points. But an earlier hand tally confirmed Mr. Biden’s lead in the state, which was over 12,000 votes, and state officials said the recount was highly unlikely to change the outcome.

Some people on Twitter and Parler, a social media site that has become a haven for conservatives, have acknowledged that diverting votes from the state’s two Republican senators, Kelly Loeffler and David Perdue, would hurt their chances against their Democratic opponents in the runoff elections on Jan. 5.

But some Trump supporters said they should “punish” Ms. Loeffler and Mr. Perdue for not more firmly supporting or investigating Mr. Trump’s baseless claims that machines using Dominion Voting Systems software had altered votes in the presidential election.

“This is really simple: the GOP in every swing state (all of which were rightfully won by Donald Trump) must ensure that their electors cast their votes for the rightful winner,” tweeted Pete D’Abrosca, who unsuccessfully tried to run for a U.S. House seat in North Carolina in 2020. “If the @GOP fails to do this, we will punish Purdue and Loeffler in Georgia.”

Representatives for the Loeffler and Perdue campaigns did not immediately respond to a request for comment.

Donald Trump Jr., the president’s son, pushed back on the idea on Monday.

Those hoping for the election of Jon Ossoff and the Rev. Raphael Warnock, the Democratic nominees, have also co-opted the #WriteInTrumpForGA hashtag. Many have posted tongue-in-cheek tweets to encourage Trump supporters to write in the president’s name or to boycott the runoff altogether to protest the baseless fraud claims. Doing so would improve the Democrats’ chances.

“I heard that when Republicans write-in ‘Trump’ for Ossoff/Warnock in Georgia, they own the libs!” one user tweeted.

A Twitter spokesman said posts related to the write-in hashtag did not violate the company’s civic integrity policies and would not be labeled. Twitter is no longer adding warning labels to tweets about the outcome of the presidential election because it has already been called, the spokesman said.