Context. The currents carried by the jets of active galactic nuclei (AGNs) can be probed using maps of the Faraday rotation measure (RM), since a jet current will be accompanied by a toroidal magnetic field, which will give rise to a systematic change in the RM across the jet. Aims. The aim of this study is to identify new AGNs displaying statistically significant transverse RM gradients across their parsecscale jets, in order to determine how often helical magnetic fields occur in AGN jets, and to look for overall patterns in the implied directions for the toroidal field components and jet currents. Methods. We have carried out new analyses of Faraday RM maps derived from previously published 8.1, 8.4, 12.1 and 15.3 GHz data obtained in 2006 on the NRAO Very Long Baseline Array (VLBA). In a number of key ways, our procedures were identical to those of the original authors, but the new imaging and analysis differs from the original methods in several ways: the technique used to match the resolutions at the different frequencies, limits on the widths spanned by the RM gradients analyzed, treatment of core-region RM gradients, approach to estimation of the significances of the gradients analyzed, and inclusion of a supplementary analysis using circular beams with areas equal to those of the corresponding elliptical naturally weighted beams.Results. This new analysis has substantially increased the number of AGNs known to display transverse RM gradients that may reflect the presence of a toroidal magnetic-field component. The collected data on parsec and kiloparsec scales indicate that the current typically flows inward along the jet axis and outward in a more extended region surrounding the jet, typical to the current structure of a co-axial cable, accompanied by a self-consistent system of nested helical magnetic fields, whose toroidal components give rise to the observed transverse Faraday rotation gradients. Conclusions. The new results presented here make it possible for the first time to conclusively demonstrate the existence of a preferred direction for the toroidal magnetic-field components -and therefore of the currents -of AGN jets. Discerning the origin of this current-field system is of cardinal importance for understanding the physical mechanisms leading to the formation of the intrinsic jet magnetic field, which likely plays an important role in the propagation and collimation of the jets; one possibility is the action of a "cosmic battery".