The invention is directed to an actuator which is mounted on a base to rotate a rotary member about a rotational axis thereof. The actuator includes a first magnetic rotary member which is rotatably mounted on the base about the axis, and provided with a first engaging portion which traces a peripheral locus about the axis. It also includes a second magnetic rotary member which is rotatably mounted about the axis, and provided with a second engaging portion engageable with the first engaging portion on the peripheral locus about the axis. The first engaging portion is moved to be engageable with the second engaging portion when the first rotary member is rotated in one direction relative to the second rotary member, and the first engaging portion is moved to be away from the second engaging portion when the first rotary member is rotated in the opposite direction. A solenoid is concentrically mounted about the axis in stationary relationship with the base, and adapted for exciting the first and second rotary members to form a magnetic path therewith when the first and second engaging portions engage with each other. And, a rotating device such as a motor is provided for rotating the first rotary member about the axis.