The 29-year-old will help ease The Dragons' goalkeeping crisis, with Michael Ingham sidelined with a hamstring problem.
"We have been looking for another experienced player and for a keeper it could well prove crucial to us in our present predicament," Wrexham boss Brian Carey told the club's official website.
"He is keen to join us and we certainly want players who are up for the fight ahead."
Welshman Williams is ready for the challenge of trying to keep Wrexham in League Two this season.
"When the offer was made to join Wrexham I didn't need asking twice," he added.
"I'm keen to do what I can to help us stay in the Football League - Wales can't afford to lose another club and from the squad there I'm sure it won't come to that."
Meanwhile, Carlisle manager Neil McDonald hopes Williams will see more first-team action at the Racecourse Ground.
McDonald said: "This could be a good move for him, as it will give him the chance for first-team football, which is what every player wants.
"He has worked really hard for us behind the scenes this season, and we wish him all the best with this move."
Sky Sports.