Only particles that carry electric charge can have a direct vertex with photons. Neutrinos are electrically neutral and accordingly they *cannot* directly couple to photons. This is nothing to do with whether the particles are massive, or not (although we do not know any massless particles that are electrically charged, at least not at low temperatures).
However, there are higher order processes which are caused by quantum corrections (so-called loop diagrams). Such quantum corrections could induce processes like, e.g., the annihilation of one neutrino and one anti-neutrino into two photons or the decay of a heavier neutrino species into a lighter one plus a photon (this is possible since we know that there are three active neutrinos, out of which at least two are massive).