The 21-year-old Huddersfield-born centre-back was a regular for Rangers’ under-23 side last season.
He will be at the Gallagher Stadium until January 6th, 2018 and could make his debut against Maidenhead United in the 2017/18 season opener on Saturday.
Formerly with Bolton Wanderers with whom he made two first-team appearances, he started out as a youth with Vanarama National League newcomers Leyton Orient.
Finney moved to Rangers last November.