Carney has several years of non-League experience under his belt following spells at Lancaster City, Bamber Bridge, Northwich Victoria, Squires Gate and Kendal Town.
He returned to Lancaster last December and was handed the captain's armband.
Carney will be available for the curtain raiser to the new season when County take on Alfreton Town at Edgeley Park this Saturday.
Manager James Gannon said: "Craig has trained with us from day one and has shown over pre-season that he's equipped to play a role with us this season. Like many of the players we've recruited, he has proven experience at a decent non-league level, but shows a real potential to develop further. He has fantastic fitness levels and a range of skills that allow him to be a versatile attacking midfielder. His pre-season goals and assists have caught the eye and shown that Craig can provide a different dimension in the team's midfield and attacking shape."
Carney has scored twice in pre-season, with goals in the 4-1 win over a young Blackburn Rovers side and in the 3-0 win at Cheadle Heath Nomads.
Although his initial terms are non-contract, Gannon says it could become a more concrete arrangement later in the year. He said: "We feel that Craig has the potential to establish himself further at the club, and his signing gives us the confidence that we now have a squad with greater depth and balance which will be very important in the opening months of the season as we compete to establish a place in the league pecking order and challenge in the FA Cup. A consideration has also been looking forward over the season and ensuring that we have the depth to cover for the potential departure of Gary Stopforth to Australia in January."
He added: "Initially when I planned out the squad for the season I wanted to have a twenty-man squad with seventeen or eighteen more experienced players to add to the young developing professionals at the club. We felt that the extra player we would need to add to our 19 pros would be an attacking midfielder. On paper our options in both wide and attacking midfield areas were already restricted, but with the injuries to Adam Thomas, Glenn Rule, Ryan Ellison and Adam Etches the concern regarding depth in this area was heightened".