Context. Resonance rings and pseudorings (here collectively called rings) are thought to be related to the gathering of material near dynamical resonances caused by non-axisymmetries in galaxy discs. This means that they are the result of secular evolution processes that redistribute material and angular momentum in discs. Studying them may give clues on the formation and growth of bars and other disc non-axisymmetries. Aims: Our aims are to produce a catalogue and an atlas of the rings detected in the Spitzer Survey of Stellar Structure in Galaxies (S4G) and to conduct a statistical study of the data in the catalogue. Methods: We traced the contours of rings previously identified and fitted them with ellipses. We found the orientation of bars by studying the galaxy ellipse fits from the S4G pipeline 4. We used the galaxy orientation data obtained by the S4G pipeline 4 to obtain intrinsic ellipticities and orientations of rings and the bars. Results: ARRAKIS contains data on 724 ringed galaxies in the S4G. The frequency of resonance rings in the S4G is of 16 ± 1% and 35 ± 1% for outer and inner features, respectively. Outer rings are mostly found in Hubble stages - 1 ≤ T ≤ 4. Inner rings are found in a broad distribution that covers the range - 1 ≤ T ≤ 7. We confirm that outer rings have two preferred orientations, namely parallel and perpendicular to the bar. We confirm a tendency for inner rings to be oriented parallel to the bar, but we report the existence of a significant fraction (maybe as large as 50%) of inner features that have random orientations with respect to the bar. These misaligned inner rings are mostly found in late-type galaxies (T ≥ 4). We find that the fraction of barred galaxies hosting outer (inner) rings is ~1.7 times (~1.3 times) that in unbarred galaxies. Conclusions: We confirm several results from previous surveys as well as predictions from simulations of resonant rings and/or from manifold flux tube theory. We report that a significant fraction of inner rings in late-type galaxies have a random orientation with respect to the bar. This may be caused by spiral modes that are decoupled from the bar and dominate the Fourier amplitude spectrum at the radius of the inner ring. The fact that rings are only mildly favoured by bars suggests that those in unbarred galaxies either formed because of weak departures from the axisymmetry of the galactic potential or that they are born because of bars that were destroyed after the ring formation. Tables A.1 and A.2 (catalogue) are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/562/A121