Shape memory alloys (SMAs) have recently emerged as promising material candidates for structural seismic resisting purposes. Most of the existing SMA-based strategies, however, are based on the wire or rod form of SMAs, where issues such as gripping complexity and fracture may exist. This paper presents a proof-of-concept study on an innovative type of SMA-based self-centring system, namely, a superelastic SMA ring spring system. The proposed system includes a series of inner high-strength steel (HSS) rings and outer superelastic SMA rings stacked in alternation with mating taper faces, where the resisting load is provided by the wedging action which tends to expand the outer rings and concurrently to squeeze the inner rings. The superelastic effect of the SMA offers energy dissipation and a driving force for recentring, and the frictional effect over the taper face further contributes to the overall resisting load and energy dissipation. The feasibility of the new system is carefully examined via numerical studies considering the parameters of ring thickness, taper angle, and coefficient of friction. The key hysteretic responses, including resisting load, stiffness, stress distributions, source of residual deformation, energy dissipation, and equivalent viscous damping, are discussed in detail. The behaviour of the SMA ring springs is also studied via analytical models, and the analytical predictions are found to agree well with the numerical results. Finally, two practical applications of the new system, namely self-centring HS-SMA ring spring connections, and self-centring SMA ring spring dampers, are discussed via comprehensive numerical studies.