The 24-year-old arrives at the Racecourse Ground on loan from League Two side Tranmere Rovers until the end of the season.
Stockton came through the youth setup at Prenton Park before spells with Morecambe and Carlisle United, before re-joining Rovers for their first season back in the Football League.
Speaking to the club's website, Graham Barrow admitted he was keen to give himself more options.
“Cole is a different type of striker to Jason Oswell who signed on Saturday so that gives us more options in that department now," he said.
“Cole did very well in this division for Tranmere in his last spell there and he knows exactly what is required to challenge at the top end of the table.
"I’m delighted he’s here. Hopefully he’ll be available to play on Tuesday.”
Stockton's first game back in the National League could well be tomorrow night against Bromley.