The effects of electron-electron interaction of a two-electron nanoscopic ring on the energy levels and far-infrared spectroscopy have been investigated based on a model calculation that is performed within the exactly numerical diagonalization. It is found that the interaction changes the energy spectra dramatically, and also shows significant influence on the far-infrared spectroscopy. The crossings between the lowest spin-singlet and triplet states induced by the Coulomb interaction are clearly revealed. Our results are related to the experiment recently carried out by Lorke et al.