U.S. District Court Judge Lance Walker rejected all of Poliquin's constitutional challenges in a 30-page decision issued last week from the Margaret Chase Smith Federal Building in Bangor.
The two-term Republican filed his appeal to the 1st U.S. Circuit Court of Appeals in Boston on Monday.
Poliquin won the plurality vote for Maine's 2nd Congressional District, but didn't earn a majority. That triggered a ranked-choice runoff, and he lost his seat to State Rep. Jared Golden.
After Walker made his ruling, Poliquin issued a statement on Twitter saying the issue "goes far beyond one election."
Mainers have approved ranked-choice voting at the polls twice.
Representative-elect Golden is preparing to be seated on Jan. 3 as part of the 116th Congress.