Gibson, 23, has arrived at his hometown club from Chester and Wirral League side Helsby FC, and made his Linnets debut against Ramsbottom United at the start of December.
Boss Michael Ellison told the club’s official website: "Ryan has recently got back into playing football locally. He's a good lad with pace to burn and an eye for goal. We got him over the line last Saturday morning (before the Ramsbottom game).
"We've only one striker at the club at the minute so that's something we know we need to improve but are finding it very difficult to do so."
Former Kendal Town and Northwich Victoria goalkeeper Tom Scott has also joined the Linnets squad, and he made himself an instant hero with two penalty saves in the recent shootout success at Hyde United.
Meanwhile, striker Connor McCarthy has departed the Millbank Linnets Stadium for Warrington Town, making his second debut for the Yellows on Saturday.
Ellison added: "Connor has left us to go to Warrington. We're sorry to see him go but understand his reasons why, with the lure of Premier football.
"He's been a breath of fresh air on and off the pitch and it's been a pleasure to work with him over these last couple of months. We wish him all the best with his new challenge at Warrington, who I have to say have conducted themselves superbly and went about things in the right way."
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