The Afar triple junction accustoms the diverging plate dynamics between the Arabian, Nubian, and Somalian plates along the Red Sea, Gulf of Aden, and East African rifts. The average anisotropy obtained from shear-wave splitting measurements agrees with the surface motion recovered by geodetic analyses. However, the vertical layering of anisotropy in this region is yet to be accurately determined. Here, we use earthquake seismic data to map Rayleigh-wave azimuthal anisotropy in the crust and lithospheric mantle beneath the East African Rift System. Our results suggest that a layering of anisotropy is present around the East African Rift System. At shorter periods that sample the crust, rift-parallel anisotropy is present in the vicinity of the rift, but in the central part of the rift, rift-normal anisotropy is found. At longer periods, sampling the lithospheric mantle, the anisotropic pattern is quite different. These observations suggest that the crust and lithospheric mantle are mechanically decoupled beneath the environs of the East African Rift System. Similarly, these results suggest complex dynamics within the crust and lithosphere in the region of the Afar triple junction.