In this paper, we present a simple method to fabricate ultra-high-density hexagonal arrays of ferromagnetic nanorings having 13 nm outer diameter, 5 nm inner diameter and 5 nm thickness. Cobalt magnetic nanorings were fabricated using a self-assembled diblock copolymer template with an angular evaporation of metal followed by an ion-beam etching. Magnetic measurements and theoretical calculations suggest that, at low fields, only the single domain and vortex states are important for rings of this size. The measured magnetization as a function of applied field shows a hysteresis that is consistent. These ultrasmall ferromagnetic rings have potential use in magnetic memory devices due to the simplicity of the preparation coupled with the ultra-high-density and geometry-controlled switching. This fabrication technique can be extended to other materials for applications in optics, sensing and nanoscale research.