Is the photon paramagnetic?

A photon exhibits a tiny anomalous magnetic moment $\mu_{\gamma}$ due to its interaction with an external constant magnetic field in vacuum through the virtual electron-positron background. It is paramagnetic ($\mu_{\gamma}>0$) in the whole region of transparency, i.e. below the first threshold energy for pair creation and has a maximum near this threshold. The photon magnetic moment is different for eigenmodes polarized along and perpendicular to the magnetic field. Explicit expressions are given for $\mu_{\gamma}$ for the cases of photon energies smaller and closer to the first pair creation threshold. The region beyond the first threshold is briefly discussed.