We studied the angular dependence of the anisotropic magnetoresistance (AMR) of the LaAlO₃/SrTiO₃ (111) interface at various gate voltages. A six-fold AMR contribution appears for high carrier concentration, which can be explained by a phenomenological AMR model for hexagonal crystal. The presence of this six-fold anisotropy along the in-plane hexagonal crystal axes of (111) interface indicates the crystalline nature of the observed AMR. Moreover, we observed an additional uniaxial AMR contribution, possibly due to the domain boundaries present in SrTiO₃.