Owing to the inherited structural defects of recycled aggregate concrete (RAC), such as deficiencies in durability and mechanical properties, its further applications in modernized civil engineering practices are significantly limited. To this end, this study aims to achieve the sustainable application of RAC and improve its mechanical properties by infilling it into the steel tube to form the recycled aggregate concrete filled steel tubular columns (RA-CFST columns). Numerous studies have indicated that embedding steel spiral stirrups inside the steel tube is helpful in improving the ultimate strength (Nu) and ductility of square CFST columns. Thus, this paper designed several square RA-CFST columns confined by high-strength steel (HSS) spiral stirrups (HSS-RA-CFST columns) and their concentric and eccentric compression behavior were experimentally studied. The test specimens were divided into two different parts, including (i) axial compression and (ii) eccentric compression test specimens. For the former, 16 columns were designed, including 4 traditional non-confined RA-CFST columns, 4 normal-strength steel (NSS) spiral-confined RA-CFST columns (NSS-RA-CFST columns), and 8 HSS-RA-CFST columns. For the latter, 8 specimens were prepared, including 2 non-confined and 6 HSS-RA-CFST columns. Effects of the critical test parameters, such as the steel tube thickness, steel spiral pitch, replacement ratio of recycled aggregate (RA) to natural aggregate (NA), and eccentricity ratio on the compression behavior of the specimens were examined. Subsequently, the failure modes, load-deflection responses, strain distributions, ductility, and the composite confinement mechanism of the columns were comprehensively studied. Finally, this paper also suggested the improved design models in predicting the Nu of the spiral-confined CFST columns (i.e., NSS-RA-CFST and HSS-RA-CFST columns), and the effectiveness and accuracy of the recommended design models were validated by using the experimental results acquired from this study and those studies collected from the literature. This study could serve as the experimental and theoretical references for the mechanical properties and determination of the Nu for the spiral confined-RA-CFST columns under both the concentric and eccentric compression.