A former Northern Ireland under-19 international, McKenna joined Stockport in July.
He made his professional debut for Carlisle United in 2010, before moving on loan to Scottish side Annan Athletic where he made nineteen appearances.
He has great experience at County’s level, having clocked up more than 100 appearances in the National League North for Bradford Park Avenue, Workington AFC and Stalybridge Celtic.
McKenna joined Southport in November 2016 but left the Merseyrail Community Stadium at the end of the season, after scoring 2 goals in eighteen National League appearances for the Sandgrounders.
Stockport manager Jim Gannon told his club`s official website: “Ben has been a good addition to the squad but with the return to fitness of players such as Adam Thomas, Matty Warburton and Darren Stephenson, Ben’s chances in the first-team will be limited.
“I am also conscious of the need to promote some of our younger talent into the squad, such as Adam Etches and George West, who both deserve an opportunity”.