With MIMO, Wi-Fi led the way to the adoption of antenna array signal processing techniques for fine-grained localization using commodity hardware. These techniques, previously exclusive to specific domains of applications, will spur interest to reach beyond localization, and now allow to consider estimating the device’s orientation in space, that once required other sources of information. Wi-Fi’s popularity and the availability of metrics related to channel propagation (CSI), makes it a candidate readily available for experimentation. Accordingly, we propose the ORION system to estimate the orientation (heading and yaw) of a MIMO Wi-Fi equipped object, relying on a joint estimation of the angle of arrival and the angle of departure. Although the CSI’s phase data is plagued by several phase inconsistencies, we demonstrate that an appropriate phase compensation strategy significantly improves estimation accuracy. By feeding the estimation to a Kalman filter, we further improve the overall system accuracy, and lay the ground for an efficient tracking. Our technique allows estimating orientations within high precision (millimeter-level).