Neutrino Magnetic Moment and the Process $\nu e \rightarrow \nu e \gamma$

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.