Barcham, 24, has penned a two-year deal at Glanford Park after leaving the League Two Gills when his contract ran out this summer
He is the Iron's second signing of the day, coming shortly after the capture of winger Jimmy Ryan from Accrington.
Alan Knill, the Iron's manager, opened his transfer dealings last week with the signing of former Sheffield United striker Jordan Robertson.
Barcham came through the youth setup at Tottenham Hotspur, before moving to the Gills for the start of the 2009/10 season.