  Using the latest quark Sivers functions extracted from the global analysis of
available data on single transverse spin asymmetry (SSA), we calculate the SSA
of Drell-Yan inclusive production of lepton pairs of invariant mass $Q$ at both
$4<Q<9$ GeV and $Q\sim M_Z$ in $p^\uparrow p$ collisions at RHIC energies. We
find that the features of the asymmetry $A_N$ for $Q\sim M_Z$ are significantly
different from that when $4<Q<9$ GeV. The $A_N$ near $Z^0$ pole is positive and
sizable in the central rapidity region while the $A_N$ at low $Q$ is negative
and only sizable in the forward rapidity region. We show that the size of $A_N$
is sufficiently large for a wide range of $Q$ around the $Z^0$ pole, and even
with the lepton pair's invariant mass integrated from Q=70 GeV to 110 GeV, the
$A_N$ is still close to 10 percent for the central and near forward rapidity
region. We argue that the SSAs of Drell-Yan inclusive dilepton production at
low $Q$ and that near the $Z^0$ pole provide complementary information for
testing the time-reversal modified universality (the sign change) of the Sivers
functions.
