Magnetic anisotropy critically determines the utility of magnetic nanocrystals (NCs) in new nanomagnetism technologies. Using angular-dependent electron magnetic resonance (EMR), we observe magnetic anisotropy in isotropically arranged NCs of a nonmagnetic material. We show that the shape of the EMR angular variation can be well described by a simple model that considers magnetic dipole-dipole interactions between dipoles randomly located in the NCs, most likely due to surface dangling bonds. The magnetic anisotropy results from the fact that the energy term arising from the magnetic dipole-dipole interactions between all magnetic moments in the system is dominated by only a few dipole pairs, which always have an anisotropic geometric arrangement. Our work shows that magnetic anisotropy may be a general feature of NC systems containing randomly distributed magnetic dipoles.