Slew, formerly of Sheffield United and Blackburn, was a free agent after leaving Cambridge and he has put pen to paper on a deal until the end of the season.
The 23-year-old was at Bramall Lane at the same time as both Spireites manager Danny Wilson and his assistant Chris Morgan
"Jordan was unattached and he's been training with us for a few weeks," said Wilson
"I've known him since his young days and I know what he's capable of doing, so from that point of view, it was a no-brainer to bring him in
"It's down to him to prove that he's worthy of a contract."
Slew started his career at Sheffield United before earning a move to then-Premier League side Blackburn in a £1.1million deal in the summer of 2011.
He never got going at Rovers and a series of loan spells followed before joining Cambridge on a permanent deal in February 2015.
Source : PA
