We present a sum-rule calculation of the decay constants of the charmed vector mesons D⁎ and Ds⁎ from the two-point correlator of vector currents. First, we show that the perturbative expansion in terms of the pole mass exhibits no sign of convergence whereas the reorganization of this expansion in terms of the MS bar mass leads to a distinct hierarchy. Second, making use of the operator product expansion in terms of the MS bar mass, we determine the decay constants of the D⁎ and DSUB>s⁎ mesons with an emphasis on the uncertainties in these theoretically predicted quantities related both to the input QCD parameters and to the limited accuracy of the method of sum rules. Our results are fD⁎ = (252.2 ±22.3OPE ±4syst) MeV and f Ds⁎ = (305.5 ±26.8OPE ±5syst) MeV. For the ratios of the vector-to-pseudoscalar decay constants we report fD⁎ /fD = 1.221 ±0.080OPE ±0.008syst and f Ds⁎ /fDs = 1.241 ±0.057OPE ±0.007syst.