We obtain the approximate relativistic bound state of a spin- particle in the field of the Yukawa potential and a Coulomb-like tensor interaction with arbitrary spin–orbit coupling number κ under the spin and pseudospin (p-spin) symmetries. The asymptotic iteration method is used to obtain energy eigenvalues and the corresponding wave functions in their closed forms. Our numerical results show that the tensor interaction removes degeneracies between the spin and p-spin doublets and creates new degenerate doublets for various strengths of tensor coupling.