Former Manchester United winger Ben signed before Easter Monday's home reverse against Fleetwood Town.
He is available to play against Lincoln United this weekend.
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"I just wanted a bit of extra cover for the remaining games," said Albion boss Jim Vince.
"Ben will need to do a bit of work to get fully match fit but he's there if we need to call on him."
Thornley, 32, was most recently at Vodkat North West Counties League Division One outfit Salford City. Before that he spent a season with Bacup Borough in the same division.
He began his career at Manchester United in the early 1990s, making nine league appearances before going on to play more than 100 matches for Huddersfield Town.
His younger brother Rod has been a revelation since switching to Wincham Park from Blue Square Premier club Altrincham.
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