This paper investigates the applicability of newly developed Cu-Al-Mn shape memory alloy (SMA) bars to retrofitting of historical masonry constructions by performing quasi-static tests of half-scale brick walls subjected to cyclic out-of-plane flexure. Problems associated with conventional steel reinforcing bars lie in pinching, or degradation of stiffness and strength under cyclic loading, and in their inability to restrain residual deformations in structures during and after intense earthquakes. This paper attempts to resolve the problems by applying newly developed Cu-Al-Mn SMA bars, characterized by large recovery strain, low material cost, and high machinability, as partial replacements for steel bars. Three types of brick wall specimens, unreinforced, steel reinforced, and SMA reinforced specimens are prepared. The specimens are subjected to quasi-static cyclic loading up to rotation angle enough to cause yielding of reinforcing bars. Corresponding nonlinear finite element models are developed to simulate the experimental observations. It was found from the experimental and numerical results that both the steel reinforced and SMA reinforced specimens showed substantial increment in strength and ductility as compared to the unreinforced specimen. The steel reinforced specimen showed pinching and significant residual elongation in reinforcing bars while the SMA reinforced specimen did not. Both the experimental and numerical observations demonstrate the superiority of Cu-Al-Mn SMA bars to conventional steel reinforcing bars in retrofitting historical masonry constructions.