Jackson was signed by former Shakers boss Kevin Blackwell in the summer and made all of his nine appearances before his departure. He has now moved away from Gigg Lane in search of regular first-team football.
The 22-year-old will stay with the Imps until Boxing Day and is eligible to play in the FA Cup and FA Trophy.
Lincoln manager Gary Simpson hopes Jackson will provide Lincoln with a much-needed spark in the final third. They have scored just 17 goals in 16 games in the Skrill Premier.
"The kid has got a bit of pace and he's been playing with a club a lot higher up, which is good," said Simpson.
"He also has played for Hereford as well, so he knows what this division about.
"We've not had much pace in the forward positions. Hopefully he can open teams up and create some goalscoring opportunities."