Williams is the top-rated quarterback in the class of 2021.
The Terps are left with Josh Jackson and Lance LeGendre as their lone scholarship quarterbacks.
Pigrome played in 11 games last season, making three starts.
The Spartans are looking to become bowl eligible, while the Terps want to finish the season on a high note.
The Terps close their season Saturday in East Lansing.
The Terps have now lost six straight games.
Tyler DeSue and Max Bortenschlager were the starting quarterbacks.