The electrostatic potential generated by a point charge at rest in a simple static, spherically symmetric wormhole is given in the form of series of multipoles and in closed form. The general potential which is physically acceptable depends on a parameter due to the fact that the monopole solution is arbitrary. When the wormhole has Z2-symmetry, the potential is completely determined. The calculation of the electrostatic self-energy and of the self-force is performed in all cases considered.