Inside living cells many essential processes involve deformation of charged helical molecules and interaction between them. Actin filaments and DNA molecules with linear charge distribution -1e/0.27nm and -2e/0.34nm respectively, are important examples of charged helical molecules. On the other hand, the existence of salt concentration inside the cell environment emphasizes on the crucial role of the electrostatic interactions in biological systems. Here we consider an impermeable dielectric molecule in the solvent with a different dielectric constant. The electrostatic free energy in the problem is studied in the Debye-Huckel regime using the analytical Green function method. Using this electrostatic free energy, we study the electrostatic contribution to the twist rigidity of a double stranded helical molecule such as DNA and actin filaments. The dependence of the electrostatic twist rigidity of the molecule to the dielectric inhomogeneity, structural parameters and the salt concentration is studied. It is shown that, depending on the parameters, the electrostatic twist rigidity could be positive or negative.