Makinson, 23, featured in the club's 4-2 win over AFC Liverpool and joins following a short spell with FC United of Manchester.
He started his football career with Everton before signing for Blackburn Rovers, and has also featured for Cardiff, Warrington Town, Atherton Collieries and Colne.
Manager Simon Haworth said: "We've got a few young centre-halves but we probably needed that extra centre-half around.
"We've had a look at Matty, we'll take him in and we'll give him a chance."
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