We report on the investigation of plasmonic resonances in metallic M"obius nanorings. Half-integer numbers of resonant modes are observed due to the presence of an extra phase {\pi} provided by the topology of the M"obius nanostrip. Anomalous plasmon modes located at the non-orientable surface of the M"obius nanoring break the symmetry that exist in conventional ring cavities, thus enable far-field excitation and emission as bright modes. The far-field resonant wavelength as well as the feature of half-integer mode numbers is invariant to the change of charge distribution on the M"obius nanoring due to the nontrivial topology. Owing to the ultra-small mode volume induced by the remaining dark feature, an extremely high sensitivity as well as a remarkable figure of merit is obtained in sensing performance. The topological metallic nanostructure provides a novel platform for the investigation of localized surface plasmon modes exhibiting unique phenomena in plasmonic applications such as high sensitive detection and plasmonic nanolasers.

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