I am not sure why you want to count the rotations without contact, but if this is because you are worried that the wires can't rotate with the "tested" rotating object, then there is a special type of connector for this case. One side of the connector will rotate with the object and the rotation sensor, and the other side will be fixed, providing the wires to external processing. You may also think of having a rotation sensor attached to the object's body and providing rotation information wirelessly.
Gyroscope can provide that information easily, you can develop such a sensor in a few hours. Also if you have a special reason to be an external sensor, then you can use computer vision that can detect a marker on the rotating object. This computer vision has a limitation based on the Camera FPS.