We aim to estimate the contribution of the radial component of the Lorentz force to the gas rotation in several types of galaxies. Using typical parameters for the exponential scale of synchrotron emission and the scale length of HI gas, under the assumption of equipartition between the energies of cosmic rays and total magnetic fields, we derive the Lorentz force and compare it to the gravitational force in the radial component of the momentum equation. We distinguish the different contributions between the large-scale and the small-scale turbulent fields by Reynolds averaging. We compare these findings with a dynamical dynamo model. We find a possible reduction of circular gas velocity in the very outer parts and an increase inside a radius of four times the synchrotron scale length. Sufficiently localized radial reversals of the magnetic field may cause characteristic modulations in the gas rotation curve with typical amplitudes of 10-20 km/s. It is unlikely that the magnetic field contributes to the flat rotation in the outer parts of galaxies. If anything, it will emph{impede} the gravitationally supported rotation, demanding for an even higher halo mass to explain the observed rotation profile. We speculate that this may have consequences for ram pressure stripping and the truncation of the stellar disc.
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