Greaves, 19, joins on an initial one-month loan.
The former Doncaster Rovers under-18s captain is expected to go straight into Curtis Woodhouse's starting eleven at the weekend in the Pitching In Northern Premier League opening weekend against Hyde United.
"I’m delighted to get Anthony in on an initial one-month loan from Doncaster Rovers," said Woodhouse.
"He’s a player with great energy and tenacity. He will get some valuable game time with us that will hopefully propel him to first team football in the future with Doncaster. Anthony will go straight into the team for Saturday."
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