  The polarized antiquark distributions in the proton can be measured by
studying spin asymmetries in vector boson production in longitudinally
polarized proton-proton collisions. The STAR and PHENIX experiments at BNL RHIC
have reported first observations of single spin asymmetries in
$W^\pm$-production most recently. We compute the QCD corrections to single and
double spin asymmetries, taking account of the leptonic decay of the $W^\pm$
boson and of restrictions on the kinematical acceptance of the detectors. The
QCD corrections have only a small impact on the asymmetries, such that a
reliable extraction of the polarized antiquark distributions can be envisaged
once more precise measurements are made.
