The 31-year-old spent time on loan with Gateshead earlier this season, making 15 appearances for the Heed.
Penn joined Carlisle from York City in the summer of 2016 but made just two appearances for the club.
The former Cheltenham Town captain joins Izale McLeod and James Jenning in joining Wrexham during January.
Wrexham have signed midfielder Russell Penn until the end of the season after he left Carlisle United by mutual consent on Friday.