Based on the performance objective of “no damage in minor earthquakes, repairable damage in moderate earthquakes, replaceable in major earthquakes”, this paper proposes a novel rocking bridge structural system incorporating shape-memory-alloy (SMA) ring springs. First, a constitutive model for the SMA ring spring is developed and implemented in the open-source finite element platform OpenSees. Next, an iterative design procedure for rocking piers is proposed, using a slip-ratio metric to optimize the geometric configuration of the rocking piers. Finally, a representative bridge is selected as a case study: finite element models of a conventional bridge and an engineered cementitious composite (ECC) rocking bridge are established in OpenSees, and fragility analyses are performed for both systems. The results show that the self-locking mechanism of the SMA ring spring effectively controls the rocking amplitude of the piers, allowing safe and reliable performance. Compared with the conventional bridge, the rocking bridge demonstrates superior seismic performance and greater post-earthquake recoverability.