  By applying the Pekeris-type approximation to deal with the (pseudo or)
centrifugal term, the spin and pseudospin symmetry solutions of the Dirac
equation for the Rosen-Morse potential including a Coulomb-like tensor
potential with arbitrary spin-orbit coupling quantum number $\kappa$ are
obtained by standard method. It has been shown from the numerical results that
the degeneracies between spin and pseudospin state doublets are removed by the
tensor interaction. Special case of this potential, that is, the spin and
pseudospin solutions of the Dirac equation with the modified P\"{o}schl-Teller
potential including a tensor interaction is also considered. The results
obtained in this case show that the tensor interaction removes the degeneracies
between the members of doublets states in spin and pseudospin symmetries.
