Logan, a 21 year-old left winger, arrives following an impressive spell at Hednesford Town so far in the 2016-17 season.
He has National League experience, spending time on loan from the Dale with Southport and, most recently, Wrexham.
The Manchester-born player came through the youth system at Rochdale and made his first-team debut while still a youth player.
Football secretary Adie Towers said: “Joel is a rapidly developing talent and we’ve been watching his progress for some time. We’re excited to have signed him.”