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.