We study the connectivity principles underlying the emergence of orientation selectivity in primary visual cortex (V1) of mammals lacking an orientation map. We present a computational model in which random connectivity gives rise to orientation selectivity that matches experimental observations. It predicts that mouse V1 neurons should exhibit intricate receptive fields in the two-dimensional frequency domain, causing shift in orientation preferences with spatial frequency. We find evidence for these features in mouse V1 using calcium imaging and intracellular whole cell recordings.