  We present Monte Carlo simulations of the Sivers effect in the polarized
Drell-Yan $pp^\uparrow \to \mu^+ \mu^- X$ process at the center-of-mass energy
$\sqrt{s}=200$ GeV reachable at the Relativistic Heavy-Ion Collider (RHIC) of
BNL. We use two different parametrizations for the Sivers function, one deduced
from the analysis of Semi-Inclusive Deep-Inelastic Scattering (SIDIS) data at
much lower energies, and another one constrained by the RHIC data for the
$pp^\uparrow \to \pi X$ process at the same energy. For a given luminosity of
$10^{32}$ cm$^{-2}$ sec$^{-1}$, we explore the necessary conditions to reach a
statistical accuracy that allows to extract unambiguous information on the
structure of the Sivers function. In particular, we consider the feasibility of
the test on its predicted universality property of changing sign when switching
from SIDIS to Drell-Yan processes.
