The possibility of detecting cosmic torsion originated from large scale Lorentz violation of cosmology at cosmic scale by the shift of energy distribution for massive cosmic neutrinos in spatial-flat FRW (Friedmann-Robertson-Walker) spacetime background is discussed. Massive cosmic neutrino scattering owing to cosmic torsion leads to a shift in the peak position of their final state energy distribution at the order of $m^2/E^2$. Moreover, the Dirac and Majorana neutrino shift values differ by the vector part of the torsion in the non-minimal vector torsion coupling case.