The 28 year-old lists Leeds United, Rotherham United and Viking FK among his previous clubs.
During his career, Dewsbury-born Dawson has also played for Bradford Park Avenue, Grantham Town and Scarborough Athletic.
He has also been capped twice by Wales at U21 level.
Dawson could make his Sheepicorns debut when Pontefract Collieries visit Ingfield in the Pitching In NPL East Division on Monday 2 January.
Keep up-to-date with our exclusive email newsletters.
Subscribe