  We calculate the single-spin asymmetries $A^{W^{\pm}}_{N}$ of $W^{\pm}$
bosons produced in transversely polarized pp collisions with the valence part
of the up (u) and down (d) quark Sivers functions treated by an available
parametrization and the light-cone quark spectator-diquark model respectively,
while the sea part Sivers functions of u and d quarks treated as
parametrization. Comparing our results with those from experimental data at
RHIC, we find that the Sivers functions of sea quarks play an important role in
the determination of the shapes of $A^{W^{\pm}}_{N}$. It is shown that
$A^{W^{-}}_{N}$ is sensitive to u sea Sivers function, while $A^{W^{+}}_{N}$ to
d sea Sivers function intuitively. The results show that the contributions of u
and d sea Sivers functions are rather sizable and of the same sign, and their
signs agree with that of d valence quarks and are opposite to that of u valence
quarks.
