The 21-year-old, who can play on the wing or up front, played for Radstock Town in the Toolstation Western League last season.
Hamilton becomes Bridgwater's fifth new signing of the summer - the others being Ollie Barnes, Sam Clark, Matt Thorne and Dave Pearce.
Bridgwater finished eighteenth last season and boss Rob Dray found himself having to rebuild the side last summer after a number of players quit to play for Blue Square Bet South side Weston-super-Mare.
He believes he should only be judged on the coming season and not the past one following the upheavel during the summer months.
Meanwhile, ex-Bath City physio Dave Lukins has joined the backroom team at Bridgwater, replacing Becky Bidgood, who has stepped down because of increased work commitments.