Smith, 28, goes straight in to the squad for tonight’s EVO-STIK Premier Division home game against Hednesford Town.
The Gingerbreads have also added central defender Taylor Gray, on dual-registration from Boston United. He was on the teamsheet for Saturday’s win over Whitby Town.
Grantham have had a good start to the season and are unbeaten at home.
Manager Ian Culverhouse said: "The first half on Saturday wasn't our best performance by a long way but we managed to regroup and find a second string to our bow to get the win.
"Tuesday will be no different as this will also be a tough test, but if we can show the same character we showed in the second half for the whole ninety, we have every chance of winning."
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