A clutching jig has a pair of holding arms which has upper ends connected together, and lower ends spaced away from each other. An inner surface of each holding arm has a through mounting hole of substantially ellipse shape, for allowing a connecting pole passing therethrough and moving therein. A trough is formed at a lower surface of each holding arm and passing through the corresponding inner surface. Two sliding elements are slidably mounted to the holding arms respectively, each of which has a basic plate. The basic plate has a though hole at an upper portion thereof, for engaging with the connecting pole. Two resisting pads are disposed between outer surfaces of the holding arms and the basic plates. Each of the resisting pads has a hole at an upper portion thereof, for engaging with the connecting pole.