The 20-year-old joined Stanley following his release by Bolton in the summer and has made three first-team appearances so far.
"Stockport are a fantastic club and it's a really good place for Tom to go," said Stanley manager Paul Cook.
"He's a young lad who needs to play football. He's got great qualities and we feel he's got a future at this club.
"We don't send players out because we don't like them or we've fallen out with them, we send them out to get experience.
"Tom Eckersley is going to be a good footballer and a really good player for Accrington Stanley and him getting some vital Conference experience will do us all the world of good."