Using 7.33 fb^{-1} of e^{+}e^{-} collision data taken with the BESIII detector at the BEPCII collider, we report the first experimental study of the purely leptonic decay D_{s}^{*+}→e^{+}ν_{e}. Our data contain a signal of this decay with a statistical significance of 2.9σ. The branching fraction of D_{s}^{*+}→e^{+}ν_{e} is measured to be (2.1_{-0.9_{stat}}^{+1.2}±0.2_{syst})×10^{-5}, corresponding to an upper limit of 4.0×10^{-5} at the 90% confidence level. Taking the total width of the D_{s}^{*+} [(0.070±0.028) keV] predicted with the radiative D_{s}^{*+} decay from the lattice QCD calculation as input, the decay constant of the D_{s}^{*+} is determined to be f_{D_{s}^{*+}}=(214_{-46_{stat}}^{+61}±44_{syst}) MeV, corresponding to an upper limit of 354 MeV at the 90% confidence level.