The 23-year-old was most recently with Sky Bet League Two side Cheltenham Town and signs an initial one-year deal, with an option for a second.
Barthram spent his youth career at Tottenham Hotspur before making the move west to Swindon Town.
From there he moved to Cheltenham where, along with fellow Bluebird Asa Hall, he helped them win promotion from the Conference (National League) back to the Football League.
He made over seventy appearances for the Robins.