Recent angle-resolved photoemission spectroscopy (ARPES) experiments on cuprate superconductors provide important guidelines for a theory of electronic excitations in the stripe phase. Using a cluster perturbation theory, where short-distance effects are accounted for by exact cluster diagonalization and long-distance effects by perturbation (in the hopping), we calculate the single-particle Green's function for a striped t-J model. The data obtained quantitatively reproduce salient (ARPES) features and may serve to rule out "bond-centered" in favor of "site-centered" stripes.