A New York jury awarded Ms. Carroll nearly $5m in damages over her allegation that Mr. Trump attacked her in the 1990s.
Jurors found Mr Trump, 76, liable for battery and defamation, but not rape.
Mr. Trump denies knowing or ever meeting Ms. Carroll, 79.
His appeal comes a day after the former president called his accuser a “wack job” during a CNN town hall event.
“I swear on my children, which I never do. I have no idea who this woman is. This is a fake story,” he said.
He accused the civil trial’s presiding judge of anti-Trump bias and said that his decision not to testify in person would not have made any difference to the outcome.
The jury’s verdict marked the first time Mr. Trump, who has been accused of sexual misconduct by more than two dozen women, was found legally responsible for assault.
Ms. Carroll, a writer, and long-time advice columnist, claimed Mr. Trump raped her inside a Bergdorf Goodman dressing room and has defamed her by calling her allegation “a hoax and a lie”.
The jury of six men and three women deliberated for less than three hours on Tuesday before reaching their decision.
Mr. Trump’s lawyer Joe Tacopina told reporters outside the courtroom that it was “a strange verdict”.
“They rejected her rape claim and she always claimed this was a rape case, so it’s a little perplexing,” he said.
He added that, in Mr. Trump’s hometown of New York, where the former president is now unpopular, “you just can’t get a fair trial”.
Ms. Carroll’s lawyer Roberta Kaplan earlier expressed confidence to US media that Mr. Trump has “no legitimate arguments for appeal”.
“I’ve rarely felt more confident about an appeal than I do about this one,” she said.
Ms. Kaplan also said her client was giving “serious consideration” toward filing a new defamation suit against Mr. Trump over his latest comments on CNN.