  Polarized photon structure can be studied in the future polarized
$e^{+}e^{-}$ colliding-beam experiments. We investigate the spin-dependent
structure function of the virtual photon $g_1^{\gamma}(x,Q^2,P^2)$, in
perturbative QCD for $\Lambda^2 \ll P^2 \ll Q^2$, where $-Q^2$ ($-P^2$) is the
mass squared of the probe (target) photon. The analysis is performed to
next-to-leading order in QCD. We particularly emphasize the renormalization
scheme independence of the result.The non-leading corrections significantly
modify the leading log result, in particular, at large $x$ as well as at small
$x$. We also discuss the non-vanishing first moment sum rule of $g_1^\gamma$,
where ${\cal O}(\alpha_s)$ corrections are computed.
