The president and other plaintiffs filed notice of appeal to the 3rd US Circuit Court of Appeals on Sunday, a day after the judge issued a scathing order shooting down claims of widespread irregularities with mail-in ballots.

The case was always a long shot to stop President-elect Joe Biden's inauguration but given Pennsylvania's 20 electoral votes at stake, it was the campaign's best hope to affect the election results through the courts.

Trump's personal lawyer, Rudy Giuliani, appeared in court for the first time in decades to argue the case this past week.

US District Court Judge Matthew Brann wrote in his order that Trump had asked the court to disenfranchise almost seven million voters.

In seeking such a "startling outcome," he said, a plaintiff could be expected to provide compelling legal arguments and "factual proof of rampant corruption" but "that has not happened".

Australian Associated Press