The young goalkeeper had a loan to Oldham Athletic cancelled after signing a new deal this summer.
Peacock-Farrell was called-up to the full Northern Ireland squad in August and has also played in the Championship for Leeds.
Manager Martin Gray told his club`s official website: â€œHeâ€™s been very highly recommended. Heâ€™s big, 6`4â€, and very athletic. He has got a massive future ahead of him but he needs some real senior football now and, hopefully, we can give him the opportunity.â€
Born in Darlington, Peacock-Farrell spent seven years at Middlesbroughâ€™s youth academy before joining Leeds in 2013.
He signed his first professional contract with the Elland Road club in 2015 and agreed a new three-year deal only this summer.
He made his full Leeds debut, aged just 19, in a 1-1 draw against Queens Park Rangers in the Championship eighteen months ago.
He goes straight into the City squad for Saturdayâ€™s game at Leamington.