In the formalism of Classical Mechanics the trajectories described by a massive relativistic particle under the action of a Kepler potential can be known by solving for the inverse of the radial coordinate a second-order linear differential equation. As a result of this solution it is possible to obtain one of the conserved movement constants of the system. In this work we propose an alternative methodological approach to solve this problem by using the Hamilton-Jacobi method. To do it we first write the Hamiltonian of the system and then we identify the canonical momenta conjugated to the degrees of freedom. From the Hamilton-Jacobi equation we obtain the movement solution and we can write the angle variable as a function of an integral over the radial variable. We perform this integral for characteristic values of the angular momentum and we directly obtain the particle trajectories. Finally we study some specific trajectories for different energy and angular momentum values.