Gravitational waves admit a Stokes decomposition into intensity ($I$), circular polarization ($V$), and linear polarization ($Q$, $U$), analogous to Cosmic Microwave Background (CMB) polarimetry. We implement a full-Stokes maximum-likelihood SGWB map-making analysis for ground-based detector networks, promoting the standard cross-correlation data products used in existing pipelines to a joint reconstruction of $I$, $V$, $Q$, $U$. Applied to LVK O3 data, we place the first constraints on the polarized angular spectra $C_{\ell }^{VV}$, $C_{\ell }^{EE}$, $C_{\ell }^{BB}$ and $|C_{\ell }^{IV}|$. We show that an intensity-only model is biased when polarized sky components are present, since the detector-network Fisher inner product does not generally make the Stokes responses orthogonal. For transient CBC foregrounds, polarized shot noise is not parametrically suppressed relative to ordinary CBC intensity shot noise. The full Stokes framework separates the Stokes sectors while providing access to polarized anisotropies invisible to conventional intensity-only searches.