Rovers land full back
The 26-year-old has impressed Pirates manager Ian Atkins since linking up with the club for pre-season training.
Beswetherick headed for The Memorial Stadium after being released by Sheffield Wednesday at the end of last season.
The former Plymouth Argyle defender shone during Rovers' pre-season friendlies, particularly in the Isle of Man tournament.
His displays curried favour with Atkins who has rewarded Beswetherick with a three-month contract with the League Two club.
Atkins has been taken by Beswetherick's versatility and the left-sider will be looking to earn a longer stay with The Pirates.