The rotational dynamics of aqueous colloidal dispersions of magnetic nanoparticles is examined whilst increasing the volume fraction up to the formation of a macroscopic solid. The freezing of the rotation is studied by magneto-optical relaxation experiments and related to small-angle neutronscattering results showing that the structure, albeit imposed by the Coulombic repulsion, remains amorphous because of the size polydispersity. The volume fraction at which the freezing occurs is noticeably dependent on the salinity of the suspension. The latter point is discussed together with the microscopic mechanism of the arrest.