We report strong experimental evidence of the optical anisotropy in a CdTe-based microcavity: the polarization of light is pinned to one of the crystallographic axes independently of the polarization of the excitation. The polarization degree depends strongly on the excitation power, reaching almost 100% in the stimulated regime. The relaxation time of the polarization is about 1 ns. We argue that all of this is an effect of a splitting of the polariton doublet at k = 0. We consider different sources for the splitting and conclude that the most likely one is optical birefringence in the mirrors and/or the cavity.