Birchall previously featured for Runcorn Linnets and Northwich Victoria, prior to his time at the KMJ Mortgages Stadium.
The Greens currently sit 14th in the Pitching In NPL West Division ahead of Saturday's game at home to Vauxhall Motors.
It is hoped the young striker will add to a forward line that has notched just seven goals in eight league matches - the fourth-lowest tally in the division this season.
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