  A sensitivity study for the search for the charged lepton flavor violating
process $\tau \to \gamma\mu$ at the Super $\tau$-Charm Facility is performed
with a fast simulation. With the expected performance of the current detector
design and an integrated luminosity of \SI{1}{ab^{-1}} corresponding to
one-year of data taking, the sensitivity on the branching fraction (BF) of
$\tau \to \gamma\mu$ is estimated to be at the level of \num{e-8}. The
sensitivity under different detector performances are also studied. With ideal
performance, the BF could be probed to be \num{2.8e-8} at \SI{90}{\percent}
confidence level. The sensitivity is expected to scale with the square root of
the luminosity, therefore with a total luminosity of \SI{10}{ab^{-1}}
corresponding to ten-year of data taking, the sensitivity could reach
\num{8.8e-9}, which is about one order of magnitude improvement upon the
current best upper limit.
