We have performed a search for the lepton-flavor-violating decay $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}$ using a data sample of $86.3\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ accumulated by the Belle detector at KEK. No evidence for a signal is seen, and we set an upper limit for the branching fraction of $\mathcal{B}(\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma})l3.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ at the 90% confidence level.
