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We start from the analytical expression of the eigenvalues $\kappa^{(i)}$ ofthe photon self-energy tensor in an external constant magnetic field $B$calculated by Batalin Shabad in the Furry representation, and in the one-loopapproximation. We expand in power series of the external field and in terms ofthe 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 generalexpression is given for the photon anomalous magnetic moment $\mu_{\gamma}>0$in the region of transparency, below the first threshold for pair creation, andit is shown that it is positive, i.e. paramagnetic. The results of thenumerical calculation for $\mu_{\gamma}>0$ are displayed in a region close tothe threshold.

Series expansion of the photon self-energy in QED and the photon anomalous magnetic moment