His attorney Thomas Van Flein filed the paperwork Monday morning.
Miller lost a round in state court on Friday, when Judge William Carey ruled that election workers did nothing wrong when they considered voter intent when counting write-in ballots for Senator Lisa Murkowski.
Carey also said there was no evidence of voter fraud.
The Supreme Court has set Friday afternoon for oral arguments in the case.
If Miller had not filed the appeal Monday, a federal stay on certifying the election results would have been lifted and the state would have certified Sen. Lisa Murkowski's victory.
“The timeline would go this way. If the federal court allows us to certify and the state Supreme Court holds the Superior Court decision, then the election would be certified. That does not mean that Mr. Miller can't then ask for a recount,” said Lt. Gov. Mead Treadwell.
“If there had been one claim where the judge was less-than-unequivocal on it, I think people might look at it and say there might be a point there that needs to be pursued. There simply hasn't been anything,” said Sen. Lisa Murkowski.