The forward, 20, joined the Iron from Accrington Stanley in the summer. He has made one start and 11 substitute appearances.
With Kevin McDonald, Freddie Sears and Dany N'Guessan all providing temporary attacking options at Glanford Park, Grant has found himself drifting away from the first-team picture.
The club stressed that his loan move "is purely to allow the Liverpudlian to get some game time under his belt, with boss Ian Baraclough still viewing him as one for the future".
Grant becomes the second Iron player on loan at Spotland, with Josh Lillis currently the club's first-choice keeper on a loan until January.