Atkinson, 22, who made seven appearances for the Cumbrians at the end of last season, turned his loan move from Middlesbrough into a permanent one last week when he signed a short-term deal.
“My target is to prove myself and to play as many games as I can,” he told the club’s official website.
“I’ve got to show the gaffer what I can do so I make sure I get another contract.”
Atkinson, who can play anywhere across the back four, added: “Hopefully I can repay the gaffer by helping the team get up the table next season.
“I get on with all of the lads and I know this is a good club, because I’ve obviously been here before, so that made the decision easier and my appearances here last season gave me a taste of what League Two is about.”