The Gross-Pitaevskii equation for Bose-Einstein condensates of exciton polaritons in two-dimensional traps is solved analytically accounting for spin-dependent polariton-polariton interactions. We show that the ground state of the condensate is characterized by a nonuniform vector polarization. Also, an analysis of the polarization degree of the condensate is performed as a function of the number of polaritons in the trap.