We present the detection of an enormous disc of cool neutral hydrogen (H i) gas surrounding the S0 galaxy NGC 612, which hosts one of the nearest powerful radio sources (PKS 0131-36). Using the Australia Telescope Compact Array, we detect MH i = 1.8 × 109 M⊙ of H i emission-line gas that is distributed in a 140-kpc wide disc-like structure along the optical disc and dust lane of NGC 612. The bulk of the gas in the disc appears to be settled in regular rotation with a total velocity range of 850 km s-1, although asymmetries in this disc indicate that perturbations are being exerted on part of the gas, possibly by a number of nearby companions. The H i disc in NGC 612 suggests that the total mass enclosed by the system is Menc ≈ 2.9 × 1012 sin-2 i M ⊙, implying that this early-type galaxy contains a massive dark matter halo. We also discuss an earlier study by Holt et al. that revealed the presence of a prominent young stellar population at various locations throughout the disc of NGC 612, indicating that this is a rare example of an extended radio source that is hosted by a galaxy with a large-scale star-forming disc. In addition, we map a faint H i bridge along a distance of 400 kpc in between NGC 612 and the gas-rich (MH i = 8.9 × 109 M ⊙) barred galaxy NGC 619, indicating that likely an interaction between both systems occurred. From the unusual amounts of H i gas and young stars in this early-type galaxy, in combination with the detection of a faint optical shell and the system's high infrared luminosity, we argue that either ongoing or past galaxy interactions or a major merger event are a likely mechanism for the triggering of the radio source in NGC 612. This paper is part of an ongoing study to map the large-scale neutral hydrogen properties of nearby radio galaxies and it presents the first example of large-scale H i detected around a powerful Fanaroff-Riley type II (FR-II) radio galaxy. The H i properties of the FR-II radio galaxy NGC 612 are very similar to those found for low-power compact radio sources, but different from those of extended Fanaroff-Riley type I (FR-I) sources.