  We investigate the Sivers asymmetry in the pion-induced single polarized
Drell-Yan process in the theoretical framework of the transverse momentum
dependent factorization up to next-to-leading logarithmic order of QCD. Within
the TMD evolution formalism of parton distribution functions, the recently
extracted nonperturbative Sudakov form factor for the pion distribution
functions as well as the one for the Sivers function of the proton are applied
to numerically estimate the Sivers asymmetry in the $\pi^- p$ Drell-Yan at the
kinematics of the COMPASS at CERN. In the low $b$ region, the Sivers function
in $b$-space can be expressed as the convolution of the perturbatively
calculable hard coefficients and the corresponding collinear correlation
function, of which the Qiu-Sterman function is the most relevant one. The
effect of the energy-scale dependence of the Qiu-Sterman function to the
asymmetry is also studied. We find that our prediction on the Sivers
asymmetries as functions of $x_p$, $x_\pi$, $x_F$ and $q_\perp$ is consistent
with the recent COMPASS measurement.
