Gritton was released by Lincoln earlier this month after a generally unhappy time at Sincil Bank.
Having enjoyed success whilst out on loan at Mansfield, the striker was expected to make his move permanent only to fall out with Stags boss Billy Dearden to scupper any deal.
As a free agent, the former Torquay man was linked with a return to the Devon side but opted against playing non-league football after The Gulls relegation.
Having only just survived the drop, Macclesfield boss Paul Ince is keen to add extra firepower to his squad, with Gritton likely to be joined by another new striker at the club in the next few weeks.
Good luck for next season