A rotation transmission device includes a roller clutch unit for selectively engaging an inner member mounted on a rotary shaft with an outer ring through rollers, and an electromagnetic clutch unit for electromagnetically controlling the selective engagement by the rollers. The current until the clutch engages is set so as to correspond to a state in which a maximum current according to the revolving speed is required and is varied according to the revolving speed of the rotary shaft to reduce power consumption and the size of the electromagnetic coil.