Metropolis Monte Carlo (MC) Brownian dynamics simulations are performed to determine the anisotropy of the electrical polarizability Delta alpha of a model DNA fragment in aqueous salt solutions. A 64 base-pair fragment of the double-stranded DNA is modeled as an impenetrable cylinder and placed in a spherical MC cell. Taking into consideration the contribution of colons to the electroneutrality condition, at every simulation step we obtain a list of counterions which constitute the net charge that compensates the polyion charge. According to the fluctuation-dissipation theorem, polarizability is calculated from fluctuations of the dipole moment created in the distribution of the net charge. Electric properties of polyelectrolyte solutions are reproduced: Delta alpha decreases with the addition of salt yielding a steady value comparable to the experiment.