  We derive the time-reversal modified universality for both quark and gluon
Sivers function from the parity and time-reversal invariance of QCD. We
calculate the single transverse-spin asymmetry of inclusive lepton from the
decay of $W$ bosons in polarized proton-proton collision at RHIC, in terms of
the Sivers function. We find that although the asymmetry is diluted from the
$W$ decay, the lepton asymmetry is at the level of several percent and is
measurable for a good range of lepton rapidity at RHIC. We argue that this
measurable lepton asymmetry at RHIC is an excellent observable for testing the
time-reversal modified universality of the Sivers function.
