In this letter, we investigate the ground state of two-dimensional disordered cylinders which contain spinless, interacting electrons using the Hartree-Fock approximation. Calculations of the deviation of the polarization from uniformity reveal a tendency of the charge to rearrange towards the ends of the system. The presence of disorder results in fluctuations of the deviation around its mean value, which are more pronounced when the disorder strength is of the order of the interaction between the electrons.