We consider the ground state properties of Raman-induced spin-tensor-momentum-coupled Bose-Einstein condensates trapped in a two-dimensional radially periodic potential. By simulating the Gross-Pitaevskii equations, the effects of spin-tensor-momentum coupling, detuning, and quadratic Zeeman on the ground-state phases of such a system are investigated numerically. Our results show that the system has different symmetry and a rich variety of ground state structures, such as ring, two-lobes and three-lobes, and so on, showing strong dependence on these controllable parameters.