Ms Carroll, 79, was awarded five million US dollars (£3.9 million) in damages after the federal jury trial in Manhattan which ended on Tuesday.
She sued Mr Trump, 76, in 2022 with her allegation that he raped her in a Bergdorf Goodman dressing room in the mid-1990s, and then defamed her by denying it happened.
Following a two-week trial, the jury found Mr Trump liable in the civil case for abuse and defamation but not rape, after just under three hours of deliberations.
Mr Trump’s lawyer Joseph Tacopina had previously said he would appeal the verdict.
His notice of appeal to the 2nd US Circuit Court of Appeals was filed hours after US District Judge Lewis Kaplan issued a ruling awarding Ms Carroll the judgment and closing the case.
In a televised town hall on Wednesday, Mr Trump made several disparaging comments about Ms Carroll that elicited applause and laughter from the audience of New Hampshire Republicans and independent voters who plan to vote in the state’s Republican primary.
The town hall was the first major television event of the 2024 US presidential campaign. CNN defended its decision to hold it as a chance to put Mr Trump in front of a wider audience, outside of the conservative media bubble he has largely kept to since early in his presidency.
The crowd gave him a standing ovation when he walked onstage.
Ms Carroll, a former columnist at Elle magazine, said in television interviews on Wednesday that she felt “fantastic” after the verdict.
During three days of testimony during the trial, she said Trump coaxed her into a dressing room, slammed her head into a wall, pulled down her tights and pentrated her.
She also said the 2022 post on Truth Social in which Trump called her claims a “Hoax and a lie” harmed her reputation.
Legal experts have said the appeals process could potentially take years.
The case is one of several legal woes Mr Trump is confronting as he mounts his campaign.
He pleaded not guilty last month to 34 felony counts of falsifying business records relating to a hush money payment to porn star Stormy Daniels ahead of the 2016 US election, which was aimed at suppressing publication of her claims of a sexual encounter with him.
Mr Trump separately faces two criminal investigations overseen by a US Justice Department special counsel into his keeping classified documents after leaving office and his efforts to overturn his 2020 election loss.
He also faces a criminal investigation by a county prosecutor in Georgia relating to his efforts to undo his 2020 election loss in that state.
Trump has denied wrongdoing in all those matters and has called himself the victim of a politically motivated witch hunt.