We present the measurement of the transverse single-spin asymmetry of weak boson production in transversely polarized proton-proton collisions at sqrt[s]=500 GeV by the STAR experiment at RHIC. The measured observable is sensitive to the Sivers function, one of the transverse-momentum-dependent parton distribution functions, which is predicted to have the opposite sign in proton-proton collisions from that observed in deep inelastic lepton-proton scattering. These data provide the first experimental investigation of the nonuniversality of the Sivers function, fundamental to our understanding of QCD.