A novel, chipless, Radio Frequency Identification (RFID) sensor is proposed for monitoring angular rotation. The rotation state is recovered by collecting the cross polar response of a tag, based on a periodic surface composed of a set of dipoles. The encoding mechanism allows the sensor to be very robust, even if it is applied on metallic objects, or in an environment with strong multipath. The proposed sensor does not require a large operational bandwidth. Instead, only a small set of reading frequencies are required. The number of reading frequencies required is dependent on the number of the employed dipoles. It is demonstrated that the rotation state of an object can be monitored within a span of 180 degrees, with up to a three-degree resolution, by employing a chipless RFID sensor comprising of four dipoles. The far field reading scheme and the absence of any electronics device allow the sensor to be employed in harsh environments.