Using 8‐25s period Rayleigh and Love wave phase velocity dispersion data extracted from seismic ambient noise, we (i) model the 3D shear wave velocity structure of the West Antarctic crust and (ii) map variations in crustal radial anisotropy. Enhanced regional resolution is offered by the UK Antarctic Seismic Network. In the West Antarctic Rift System (WARS), a ridge of crust ~26‐30km thick extending south from Marie Byrd Land separates domains of more extended crust (~22km thick) in the Ross and Amundsen Sea Embayments, suggesting along‐strike variability in the Cenozoic evolution of the WARS. The southern margin of the WARS is defined along the southern Transantarctic Mountains (TAM) and Haag Nunataks‐Ellsworth Whitmore Mountains (HEW) block by a sharp crustal thickness gradient. Crust ~35‐40km is modelled beneath the Haag Nunataks‐Ellsworth Mountains, decreasing to $sim$30‐32,km km thick beneath the Whitmore Mountains, reflecting distinct structural domains within the composite HEW block. Our analysis suggests that the lower crust and potentially the mid crust is positively radially anisotropic (VSH > VSV) across West Antarctica. The strongest anisotropic signature is observed in the HEW block, emphasising its unique provenance amongst West Antarctica's crustal units, and conceivably reflects a ~13,km thick metasedimentary succession atop Precambrian metamorphic basement. Positive radial anisotropy in the WARS crust is consistent with observations in extensional settings, and likely reflects the lattice‐preferred orientation of minerals such as mica and amphibole by extensional deformation. Our observations support a contention that anisotropy may be ubiquitous in continental crust.