Using e thorn e- collision data with an integrated luminosity of 7.33 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 thorn s -> mu thorn nu mu is measured to be o0.5294 0.0108stat 0.0085syst thorn %. Based on this, the product of the D thorn s decay constant fD thorn s and the magnitude of the c -> s quark mixing matrix element jVcsj is determined to be fD thorn s jVcsj 1/4 241.8 2.5stat 2.2syst MeV. Using the value of jVcsj given by the global standard model fit, fD thorn s is found to be 248.4 2.5stat 2.2syst MeV. Alternatively, using the value of fD thorn s from a recent lattice quantum chromodynamics calculation, jVcsj is determined to be 0.968 0.010stat 0.009syst.