In this study, we shed light on the properties of a photonic ring resonator made up of a closed array of circular dielectric nanorods arranged periodically in a background material. This type of resonator can reach high-quality factors (Q-factor) for specific transverse-magnetic (TM)-like modes, while maintaining a small footprint. We validate this by full 3D finite difference time domain simulations. The properties of the mode most interesting for applications are determined for various parameters of the resonator for the material parameters of GaN. This study provides design guidelines for the realization of this type of photonic nano-resonator and proposes and analyses two practical implementations.