In this paper, we present a new omnidirectional visual compass for a camera-robot, based on the phase correlation method in the 2-D Fourier domain. The proposed visual compass is accurate, robust to image noise, and frugal in the use of computational resources. Moreover, unlike the majority of existing ego-motion estimators, it does not rely on any geometric image primitive, and it only requires a minimal knowledge of the internal camera parameters. Extensive real-world experiments conducted with a hypercatadioptric camera mounted on the end-effector of a Stäubli manipulator and on a Pioneer robot, show the effectiveness of our approach.