The 29-year-old joined Wrexham in September 2013 after a period on trial following his release by Bury.
Warrington-born Carrington started his professional career with Crewe Alexandra and has also played for MK Dons and Hamilton Academical.
Carrington was one of seven players to have been offered a new deal by manager Gary Mills.
Rob Evans, Jamal Fyfield, Simon Heslop, Connor Jennings, Sean Newton and Kayden Jackson have also been offered new deals.
Mills revealed striker Jackson had turned down the offer of a new contract.
Midfielder Mark Carrington has signed a new one-year contract with National League side Wrexham.