  In this work we study the Dirac equation with vector and scalar potentials in
the spacetime generated by a cosmic string. Using an approximation for the
centrifugal term, a solution for the radial differential equation is obtained.
We consider the scattering states under the Hulth\'{e}n potential and obtain
the phase shifts. From the poles of the scattering $S$-matrix the states
energies are determined as well.
