  Utilizing $7.33~\mathrm{fb}^{-1}$ of $e^+e^-$ collision data taken at the
center-of-mass energies of 4.128, 4.157, 4.178, 4.189, 4.199, 4.209, 4.219, and
4.226 GeV with the BESIII detector, the branching fraction of the leptonic
decay $D_s^+\to\tau^+\nu_\tau$ via $\tau^+\to\mu^+\nu_\mu\bar \nu_\tau$ is
measured to be $\mathcal{B}_{D_s^+\to\tau^+\nu_\tau}=(5.34\pm0.16_{\rm
stat}\pm0.10_{\rm syst})\%$. Combining this branching fraction with the world
averages of the measurements of the masses of $\tau^+$ and $D_s^+$ as well as
the lifetime of $D_s^+$, we extract the product of the decay constant of
$D_s^+$ and the $c\to s$ Cabibbo-Kobayashi-Maskawa matrix element to be
$f_{D_s^+}|V_{cs}|=(246.2\pm3.7_{\rm stat}\pm2.5_{\rm syst})~\mathrm{MeV}$.
Taking $|V_{cs}|$ from a global fit in the standard model we obtain
$f_{D_s^+}=(252.7\pm3.8_{\rm stat}\pm2.6_{\rm syst})$ MeV. Conversely, taking
$f_{D_s^+}$ from lattice quantum chromodynamics calculations, we obtain
$|V_{cs}| = 0.984\pm0.015_{\rm stat}\pm0.010_{\rm syst}$.
