Using concrete waste as recycled aggregate (RA) in engineering structures can generate great ecological and economic benefits. To enhance the compressive properties of RA concrete (RAC), basalt fiber reinforced polymer (BFRP) tubes were used to provide lateral confinement in this study. Monotonic axial compressive tests were carried out on BFRP tube-confined RAC using 36 cylindrical specimens. Detailed test results were presented, including the failure mode, stress-strain curve, compressive strength, axial strain, and dilation property. The influences of the RA replacement ratio and the number of BFRP layers were analyzed. The test results indicated that BFRP tube-confined specimens exhibited strain hardening behavior in all of their stress-strain curves even if only a single layer of BFRP was used, and the failure was due to BFRP rupture along the hoop direction. The ultimate strength and deformability of RAC were significantly enhanced using BFRP confinement, with the confinement effect becoming more pronounced with increasing RA replacement ratios and BFRP layers. Compared to the unconfined specimens, the maximum enhancements in the ultimate strength and axial strain reached 2.8 times and 18.1 times, respectively, after BFRP confinement. Three typical theoretical models of FRP-confined concrete were employed to predict the ultimate conditions and axial stress-strain curves of the specimens. Finally, an improved model was formulated based on the test data to predict the ultimate conditions of BFRP tube-confined RAC cylinders. The proposed model was proven to predict the axial stress-strain curves, ultimate strength, ultimate axial strain with reasonable accuracy.