Bound-state solutions of the Dirac equation with Yukawa tensor interaction and Manning-Rosen potential are obtained for any arbitrary state. The energy eigenvalues and the corresponding eigenfunctions are obtained using the parametric Nikiforov–Uvarov method. Thereby, the radial wavefunctions of scattering states are obtained in terms of hypergeometric functions. Next, using the basic properties of the hypergeometric function, the phase-shifts are reported. In addition, some numerical results are included in the case of pseudospin and spin symmetry limits.