A fascia board support device features a rafter bracket having a side member for placement against one vertical side of the rafter, and a movable member pivotally coupled to the side member for movement into and out of a deployed position in which at least a portion of the movable member depends downward on an opposing side of the roof rafter. A clamping mechanism forces the depending portion against this opposing side of the roof rafter to clamp the device thereon, at which point a fascia board support projecting from the front end of the rafter bracket can seat a fascia board. After fastening of the fascia board to the rafter, the device is easily removed by releasing the clamp, flipping the movable member over to same side of the rafter as the side member and lowering the device to withdraw the support from beneath the fastened fascia board.