  We start from the analytical expression of the eigenvalues $\kappa^{(i)}$ of
the photon self-energy tensor in an external constant magnetic field $B$
calculated by Batalin Shabad in the Furry representation, and in the one-loop
approximation. We expand in power series of the external field and in terms of
the squared photon transverse momentum $z_2$ and (minus) transverse energy
$z_1=k^2-z_2$, in terms of which are expressed $\kappa^{(i)}$. A general
expression is given for the photon anomalous magnetic moment $\mu_{\gamma}>0$
in the region of transparency, below the first threshold for pair creation, and
it is shown that it is positive, i.e. paramagnetic. The results of the
numerical calculation for $\mu_{\gamma}>0$ are displayed in a region close to
the threshold.
