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

The contribution of a neutrino magnetic moment ${\mu }_{\nu }$ to the cross section of the process $\nu e^{-}\to \nu e^{-}\gamma$ 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.