An inversion method for retrieving seismic anisotropy from non-double-couple components of seismic moment tensors is presented. The method requires a set of highly accurate moment tensors of earthquakes that occurred in a homogeneous anisotropic focal area on differently oriented faults. In contrast to standard methods retrieving anisotropy from travel times or from shear wave splitting, which yield an overall anisotropy averaged along a whole ray path, the presented method yields a local value of anisotropy just in the focal area. The method is robust, being able to retrieve the orientation as well as strength of anisotropy even for low anisotropy symmetries as for orthorhombic symmetry. The method can utilize the moment tensors constrained to have zero trace, but using unconstrained moment tensors is advantageous. The method is applied to retrieving anisotropy in the Tonga subduction zone using moment tensors of deep-focus earthquakes reported in the Harvard centroid moment tensor catalog. The inversion is complemented by tests on synthetic data to assess its stability and the accuracy of the results. The inversion indicates that the subduction zone is anisotropic with orthorhombic symmetry. The orientation of the intra-slab anisotropy is defined by axes (azimuth/dip) a1 = 320¿/54¿, a2 = 121¿/38¿, and a3 = 223¿/81¿. The errors in the azimuth and dip are about 5¿. The first and second axes lie along the downdip motion of the slab and along the normal to the slab, respectively. The strength of the P, S1, and S2 anisotropy is of 7.3 ¿ 1.5%, 13.4 ¿ 2.5%, and 12.6 ¿ 3.5%, respectively. The errors of anisotropy strength are only rough estimates, which reflect random but not systematic errors in the moment tensors used in the inversion. The values for anisotropy strength in the slab are remarkably higher than those observed in the surrounding mantle. The symmetry axes of anisotropy coincide with the principal stress directions in the slab. This manifests a primary impact of stress on anisotropy formation. The retrieved anisotropy in the slab can serve as an additional constraint on its structure and mineralogical composition.