Viscous shear in the asthenosphere accommodates relative motion between Earth's surface plates and underlying mantle, generating lattice-preferred orientation (LPO) in olivine aggregates and a seismically anisotropic fabric. Because this fabric develops with the evolving mantle flow field, observations of seismic anisotropy can constrain asthenospheric flow patterns if the contribution of fossil lithospheric anisotropy is small. We use global viscous mantle flow models to characterize the relationship between asthenospheric deformation and LPO and compare the predicted pattern of anisotropy to a global compilation of observed shear wave splitting measurements. For asthenosphere >500 km from plate boundaries, simple shear rotates the LPO toward the infinite strain axis (ISA, the LPO after infinite deformation) faster than the ISA changes along flow lines. Thus we expect the ISA to approximate LPO throughout most of the asthenosphere, greatly simplifying LPO predictions because strain integration along flow lines is unnecessary. Approximating LPO with the ISA and assuming A-type fabric (olivine a axis parallel to ISA), we find that mantle flow driven by both plate motions and mantle density heterogeneity successfully predicts oceanic anisotropy (average misfit 13°). Continental anisotropy is less well fit (average misfit 41°), but lateral variations in lithospheric thickness improve the fit in some continental areas. This suggests that asthenospheric anisotropy contributes to shear wave splitting for both continents and oceans but is overlain by a stronger layer of lithospheric anisotropy for continents. The contribution of the oceanic lithosphere is likely smaller because it is thinner, younger, and less deformed than its continental counterpart.