The 24-year-old played nine games for the Mariners last term before a serious knee injury cut short his stay in Lincolnshire.
He has since battled back to fitness and spent a month on loan at his former club Barnet earlier this season.
Sinclair, who will be out of contract at The Valley in the summer, should be in the Grimsby squad for Saturday's League Two trip to Aldershot.
The Addicks have extended striker David Mooney's loan spell until the end of the season.
Source: Team Talk
