Ice crystals are mechanically and dielectrically anisotropic. They progressively align under cumulative deformation, forming an ice-crystal-orientation fabric that, in turn, impacts ice deformation. However, almost all the observations of ice fabric are from ice core analysis, and its influence on the ice flow is unclear. Here, we present a non-linear inverse approach to process co- and cross-polarized phase-sensitive radar data. We estimate the continuous depth profile of georeferenced ice fabric orientation along with the reflection ratio and horizontal anisotropy of the ice column. Our method approximates the complete second-order orientation tensor and all the ice fabric eigenvalues. As a result, we infer the vertical ice fabric anisotropy, which is an essential factor to better understand ice deformation using anisotropic ice flow models. The approach is validated at two Antarctic ice core sites (EPICA (European Project for Ice Coring in Antarctica) Dome C and EPICA Dronning Maud Land) in contrasting flow regimes. Spatial variability in ice fabric characteristics in the dome-to-flank transition near Dome C is quantified with 20 more sites located along with a 36 km long cross-section. Local horizontal anisotropy increases under the dome summit and decreases away from the dome summit. We suggest that this is a consequence of the non-linear rheology of ice, also known as the Raymond effect. On larger spatial scales, horizontal anisotropy increases with increasing distance from the dome. At most of the sites, the main driver of ice fabric evolution is vertical compression, yet our data show that the horizontal distribution of the ice fabric is consistent with the present horizontal flow. This method uses polarimetric-radar data, which are suitable for profiling radar applications and are able to constrain ice fabric distribution on a spatial scale comparable to ice flow observations and models.