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We investigate the ‘wiggled structure’ of AGN radio jets by performing 3-dimensional magnetohydrodynamic (MHD) simulations based on the ‘Sweeping Magnetic-Twist’ model. The correlation between the wiggled structures of AGN radio jets and tails and the distribution of magnetic field in them suggests that the magnetic field plays an essential role, not only in the emission of synchrotron radiation, but also in the dynamics of the production of the AGN-jets–lobes systems (core, jets, tails, lobes, and hotspots) themselves. In order to produce such a systematic magnetic configuration, a supply of a huge amount of energy, in an organized form, is necessary. We think that the supply of this energy must come from AGN core. The most natural means of carrying this energy is in the form of the Poynting flux of torsional Alfven wave train (TAWT) produced in the interaction of the rotating accretion disk and the large scale magnetic field brought into it by the gravitational contraction. The propagation of the TAWT can produce a slender jet shape by the sweeping pinch effect from the initial large scale magnetic field. Further, wiggles of the jet can be produced by the MHD processes due to the TAWT. Our numerical results reveal that the structure of the magnetic jet can be distorted due to the helical kink instability. This results in the formation of wiggled structures in the jets as the TAWT encounters a domain of reduced Alfven velocity (either towards the boundary of the ‘cavity’ from which the mass contracted to the central core, or encounting smaller and denser clouds in the domain). The toroidal component of the field accumulates due to the lowered Alfven velocity, and produces a strongly pinched region, as well as the deformation of the jet into a writhed structure. The condition for this to occur corresponds to the Kruskal–Shafranov criterion of the linear case. If the intrinsic relationship between the wiggled structure of the jet shape and the magnetic field in the jets and tails as proposed in this paper is confirmed, it will influence the understandings of the AGN jets in a vital way. Such a systematic magnetic structure in the remote part of the jets and tails cannot be explained in most of the jet models except for the sweeping magnetic-twist model on which the present paper is based.