Siddons, 28, played for Gingerbreads manager Tom Culverhouse at King's Lynn Town, where he scored 12 goals in 34 appearances last season.
A former England Under 18s international, Siddons has also played for Sleaford Town.
Culverhouse said: "He scored some crucial goals for me last season and I'm really happy to get him in the squad."
Siddons becomes the fourth "Tom" in the Grantham squad, as they prepare for their EVO-STIK Premier League game against Hyde on Saturday.
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