Using about 3.9 million hadronic Z decays from e+e- collisions recorded by the OPAL detector at LEP at centre-of-mass energies near M_Z the branching ratio for the decay D_s -> tau nu_tau has been measured to be (7.0 +/- 2.1(stat) +/- 2.0 (syst)) %. This result can be used to derive the decay constant of the D_s meson: f(D_s) = 286 +/- 44(stat) +/- 41(syst) MeV.