  We investigate the twist-3 effects in the polarized virtual photon structure.
The structure functions $g_1^\gamma$ and $g_2^\gamma$ of polarized photon could
be experimentally studied in the future polarized $ep$ or $e^+e^-$ colliders.
The leading contributions to $g_1^\gamma$ are the twist-2 effects, while
another structure function $g_2^\gamma$, which only exists for the virtual
photon target, receives not only the twist-2 but also twist-3 contributions. We
first show that the twist-3 effects actually exist in the box-diagram
contributions and we extract the twist-3 part, which can also be reproduced by
the pure QED operator product expansion. We then calculate the non-trivial
lowest moment ($n=3$) of the twist-3 contribution to $g_2^\gamma$ in QCD. For
large $N_c$ (the number of colors), the QCD analysis of the twist-3 effects in
the flavor nonsinglet part of $g_2^\gamma$ becomes tractable and we can obtain
its moments in a compact form for all $n$.
