An apparatus (10) for tightening a hexagon head bolt (13) includes a vertically movable automatic robot arm (16), a screwing mechanism (18) having a rotational part (19), a shaft member (20) mounted to the rotational part, a socket portion (21) mounted to the shaft member for receiving therein a head (14) of the bolt, and a retention means (22) for retaining the head received in the socket portion or retaining the head released from the socket portion. When the arm moves vertically with the head received in the socket portion, the rotational part is rotated along with the shaft member and the socket portion to screw the bolt into a threaded aperture (12) of a crankcase (11) of an engine.