  Using $e^+e^-$ collision data with an integrated luminosity of
$7.33~\mathrm{fb}^{-1}$ collected at center-of-mass energies between 4.128 and
4.226 GeV with the BESIII detector operating at the BEPCII collider, the
branching fraction of the leptonic decay $D_s^+\to\mu^+\nu_\mu$ is measured to
be $(0.5294\pm0.0108_{\rm stat}\pm0.0085_{\rm syst})$\%. Based on this, the
product of the $D_s^+$ decay constant $f_{D_s^+}$ and the magnitude of the
$c\to s$ quark mixing matrix element $|V_{cs}|$ is determined to be
$f_{D_s^+}|V_{cs}|=241.8\pm2.5_{\rm stat}\pm2.2_{\rm syst}~\mathrm{MeV}$. Using
the value of $|V_{cs}|$ given by the global standard model fit, $f_{D_s^+}$ is
found to be $248.4\pm2.5_{\rm stat}\pm2.2_{\rm syst}$\,MeV. Alternatively,
using the value of $f_{D_s^+}$ from a recent lattice quantum chromodynamics
calculation, $|V_{cs}|$ is determined to be $0.968\pm0.010_{\rm
stat}\pm0.009_{\rm syst}$.
