Electrodynamic tethers provide actuation for performing orbit correction of spacecrafts. When an electrodynamic tether system is orbiting the Earth in an inclined orbit, periodic changes in the magnetic field result in a family of unstable periodic solutions in the attitude motion. This paper shows how these periodic solutions can be stabilized by controlling only the current through the tether. A port-controlled Hamiltonian formulation is employed to describe the tethered satellite system and a passive input-output connection is used in the control design. The control law consists of two parts: a feedback connection, which stabilizes the open-loop equilibrium; and a bias term, which is able to drive the system trajectory away from this equilibrium, a feature necessary to obtain orbit adjustment capabilities of the electrodynamic tether. It is then shown how the periodic solutions of the closed-loop system can be approximated by power series, and a relation is found between control gain and perturbations around the open-loop solution. Stability properties of the system are investigated using Floquet analysis, and the region of stability is found in the plane defined by the control parameters.