  We study the small-$x$ behaviour of the polarized photon structure function
$F_3^{\ga}$, measuring the gluon transversity distribution, in the leading
logarithmic approximation of perturbative QCD. There are two contributions,
both arising from two-gluon exchange. The leading contribution to small-$x$ is
related to the BFKL pomeron and behaves like $x^{-1-\om_2}$, $\om_2 = {\cal
O}(\al_S)$. The other contribution includes in particular the ones summed by
the DGLAP equation and behaves like $x^{1-\om_0^{(+)}}$, $\om_0^{(+)} = {\cal
O}(\sqrt{\al_S})$.
