Ingham, who stepped up from the Under 23s to the First Team last December, making his debut in the FA Trophy, has made four appearances for the Celts.
The defender has been around the First Team squad for much of last season, as well as in the early stages of the current campaign.
He will now gain First Team experience with the Central Midlands League side, whilst remaining available for Farsley should he be required.
Good luck, Matty!