Concrete production using recycled aggregates (RAs) from construction and demolition waste is known to have a lower strength performance than natural aggregate concrete. Many studies have been carried out to improve the strength properties of recycled aggregate concrete (RAC). One widely accepted strategy is to use fiber-reinforced polymer (FRP) jackets as external confinement material to enhance the compressive strength and ductility performance of RAC, especially in the seismic retrofit of RAC members. Most existing research has focused on normal strength concrete subjected to monotonic loading. However, retrofitting or repair work is more common for concrete structures with low concrete strength. In addition, cyclic behavior research focused on FRP-confined low-strength RAC is also rare due to the lack of sufficient experimental data. In this study, 29 concrete specimens were cast using varying proportions of RAs mixed with natural coarse aggregates. In this case, poor quality natural aggregates were selected to achieve a low concrete strength. Thickness of the carbon FRP (CFRP) jacket, loading types (monotonic or cyclic), and the RAs replacement ratio were the main test parameters of this experimental work. The mechanical properties of CFRP-confined RAC were analyzed and discussed from the failure mode perspective; these included peak strength, ultimate strain, and cyclic stress-strain relationships. Test results show that strength enhancement by FRP confinement was much more pronounced in lower strength RAC than in normal strength concrete, whereas the ductility improvement was almost consistent. Confinement rigidity and recycled aggregate replacement ratio had little effect on cyclic stress-strain behavior, in terms of unloading and reloading paths, as well as in plastic strain. The adhered cement mortar on RAs weakened the impact brought by confinement when repeated unloading and reloading were applied. This was especially true during cyclic loading, which generated a large deformation.