Self-centering earthquake-resistant structures have received increased attention due to their ability to reduce post-earthquake residual deformations and, thus, repair time and cost. This stimulated the development of recentering shape memory alloy (SMA) dampers that use superelastic nitinol wires to dissipate energy and self-center the structure. However, there are still a few case study applications on full-scale RC buildings in the literature. Moreover, general guidelines or even simplified approaches for the practical design of SMA damped braces are still lacking. This paper focuses on evaluating the effect of using self-centering shape memory alloy dampers for buckling-restrained braces applied for the seismic retrofit of a complex RC building structure. A design method originally proposed for elastoplastic dampers was implemented to size the SMA dampers to be placed on selected spans and stories of a building. The effectiveness of the design procedure was demonstrated by nonlinear time-history analyses under different sets of earthquake strong ground motions. The analysis results show that the recentering shape memory alloy bracing system is effective in limiting the maximum transient inter-story drifts and reducing the residual inter-story drifts after strong seismic events, due to its excellent recentering behavior together with its not negligible energy dissipation capacity.