Feeney, 18, arrives at The Giant Axe following a short stint at Atherton Collieries, and played under City's assistant manager Graham Lancashire at Barnsley.
Lancashire said: "he’s got all the attributes to be really successful at this level.
"He’s still learning but he’s a good footballer and he’ll give us something different to our current attacking options.”
Feeney goes straight in to contention for the Lancashire Challenge Trophy game at Charnock Richard, with the likes of Matt Blinkhorn and David Norris unlikely to be selected.
Meanwhile, Rohan Roache has returned to Blackpool at the end of his 28-day loan.
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