  We perform a study of $W$-boson production in polarized proton-proton
collisions through next-to-next-to-leading order (NNLO) in perturbative QCD.
This calculation is required to extend the extraction of polarized parton
distribution functions to NNLO accuracy. We present differential distributions
at $\sqrt{s}=510$ GeV, relevant for comparison to measurements from the
Relativistic Heavy Ion Collider (RHIC). The NNLO QCD corrections significantly
reduce the scale dependence of the cross section. We compare the longitudinal
single-spin asymmetries as a function of lepton pseudorapidity to RHIC data.
The asymmetries exhibit excellent stability under perturbative QCD corrections.
