  Neutrino-photon processes, forbidden in vacuum, can take place in presence of
a thermal medium or an external electro-magnetic field, mediated by the
corresponding charged leptons (real or virtual). The effect of a medium or an
electromagnetic field is two-fold - to induce an effective $\nu-\gamma$ vertex
and to modify the dispersion relations of all the particles involved to render
the processes kinematically viable. It has already been noted that in presence
of a thermal medium such an electromagnetic interaction translates into the
neutrino acquiring a small effective charge. In this work, we extend this
concept to the case of a thermal medium in presence of an external magnetic
field and calculate the effective charge of a neutrino in the limit of a weak
magnetic field. We find that the effective charge is direction dependent which
is a direct effect of magnetic field breaking the isotropy of the space.
