  The contribution of a neutrino magnetic moment $\mu_{\nu}$ to the cross
section of the process $\nu e^{-}\rightarrow \nu e^{-} \gamma $ has been
calculated and compared with the Standard Electroweak one. The radiative
process allows to reach low enough values of $Q^2$ without the need to operate
at very small energies of recoil electrons. Regions in the phase space which
are more favourable to set bounds on $\mu_{\nu}$ are suggested.
