To achieve a graded seismic protection objective, namely, no damage under minor earthquakes, repairable damage under moderate earthquakes, and replaceable damage under major earthquakes, a novel rocking bridge system based on shape memory alloy (SMA) ring springs is proposed in this study. A constitutive model of the SMA ring springs is first developed and implemented in open-source finite element software OpenSees. An iterative design procedure for rocking piers is subsequently proposed, in which the slip ratio is adopted as an optimization index for the geometric configuration of the rocking piers. A typical bridge is then selected as a case study example. Finite element models of both a conventional bridge and an engineered cementitious composite (ECC) rocking bridge are subsequently established in OpenSees, and the seismic fragility of the two bridge systems is analyzed. The results indicate that the self-locking mechanism of the SMA ring springs effectively controls the rocking amplitude of the piers, thereby ensuring safe and reliable performance. Compared with conventional bridges, rocking bridges exhibit superior seismic performance and lower seismic fragility.