A general investigation of the electrical conductivity for radio-frequency (RF) fields in strongly magnetized plasmas with small-scale density fluctuations is performed within the cold plasma hydrodynamical approximation. It is shown that in such plasmas an RF phenomenon similar to the Bohm diffusion exists: the presence of stochastic RF electric field in a turbulent plasma can lead to a strong enhancement of the RF currents flowing in the direction of the applied electric field components transverse to the magnetic field. The appearance of these turbulent drift currents favours energy transfer from the RF fields to the plasma and thus leads to their stronger damping. This effect allows us to interpret quantitatively the enhanced damping of the magnetosonic waves observed in several experiments. The magnetized radially inhomogeneous cylindrical plasmas in these experiments are characterized by density fluctuations due to drift instabilities. The theory has also a number of other applications; an example is given of the whistlers damped by the ionospheric density fluctuation
