A circular plasmon current in a silver nanoring is demonstrated and investigated with electrodynamics theory. The circular current is driven by the incident plane electromagnetic wave. For a silver ring with a thickness of $50\mathrm{nm}$ and inner and outer diameters of 200 and $300\mathrm{nm}$ , the circular current can be obtained when the incident wavelength is at $650\mathrm{nm}$ , which is about twice the diameter of the ring. The circular current can be observed only when the incident wave and the polarization directions are both parallel to the ring plane. The resonance wavelength shifts to red with the expansion of the ring diameter and the drop in the ring thickness. The discovery holds promise for the design of artificial materials with negative refractive index in the visible wavelengths and might stimulate new ideas for the development of nanoelectronic devices.