According to the radical pair model, the magnetic compass sense of migratory birds relies on photochemical transformations in the eye to detect the direction of the geomagnetic field. Magnetically sensitive radical pairs are thought to be generated in cryptochrome proteins contained in magnetoreceptor cells in the retina. A prerequisite of the current model is for some degree of rotational ordering of both the cryptochromes within the cells and of the cells within the retina so that the directional responses of individual molecules do not average to zero. Here, it is argued that anisotropic distributions of radical pairs can be generated by the photoselection effects that arise from the directionality of the light entering the eye. Light-induced rotational order among the transient radical pairs rather than intrinsic ordering of their molecular precursors is seen as the fundamental condition for a magnetoreceptor cell to exhibit an anisotropic response. A theoretical analysis shows that a viable compass magnetoreceptor could result from randomly oriented cryptochromes contained in randomly oriented cells distributed around the retina.