  We investigate the possibility of searching the lepton-flavor-violating (LFV)
$\tau\rightarrow \mu\gamma$ rare decay at the Super Charm-Tau Factory (CTF). By
comparing the kinematic distributions of the LFV signal and the standard model
(SM) background, we develop an optimized event selection criteria which can
significantly reduce the background events. It is concluded that new $2 \sigma$
upper limit of about $1.9 \times 10^{-9}$ on $Br(\tau \rightarrow \mu \gamma)$
can be obtained at the CTF, which is beyond the capability of Super-B factory
in searching $\tau$ lepton rare decay. Within the framework of the scalar
leptoquark model, a joint constraint on $\lambda_1 \lambda_2$ and $M_{LQ}$ can
be derived from the upper bound on $Br(\tau \rightarrow \mu \gamma)$. With
$1000~ fb^{-1}$ data expected at the CTF, we get $\lambda_1\lambda_2 < 7.2
\times 10^{-2}~(M_{LQ} = 800~ {\rm GeV})$ and $M_{LQ} > 900~{\rm
GeV}~(\lambda_1 \lambda_2 = 9 \times 10^{-2})$ at $95\%$ confidence level
(C.L.).
