  We investigate the one-gluon-exchange ($\alpha \alpha_s$) corrections to the
polarized real photon structure function $g_1^\gamma(x,Q^2)$ in the massive
parton model. We employ a technique based on the Cutkosky rules and the
reduction of Feynman integrals to master integrals. The NLO contribution is
noticeable at large $x$ and does not vanish at the threshold of the massive
quark pair production due to the Coulomb singularity. It is found that the
first moment sum rule of $g_1^\gamma$ is satisfied up to the NLO.
