This paper investigates the cyclic behavior of a steel self-centering (SC) rocking column. The steel SC rocking column consists of an H-section steel column and a pair of shape memory alloy (SMA) slip-friction dampers (SMASFDs). As the kernel part, the SMASFDs enhance SC capability of the rocking column and dissipate the input energy. The working principle of the rocking column is first described, along with the analytical equations that govern the behavior under loading cycles, which are validated by experimental data. The component tests were conducted on the NiTi SMA bar and the slip-friction mechanism, separately. And then, the cyclic loading tests were conducted on a 1:2-scaled rocking column specimen. The considered axial force ratio included 0, 0.1 and 0.2. During the entire experimental procedure, the SMA bars were neither repaired nor replaced. It is found that up to a drift ratio of 7 %, the rocking column maintained stable flag-shaped hysteresis, which is characterized by excellent SC capability and satisfactory damping capacity. The testing results also indicated that increasing axial force ratio effectively increased the strength and stiffness of the rocking column, whereas it reduced the post-decompression stiffness due to the P-Δ effect. Finally, the numerical models were established in ABAQUS and OpenSees, both of which were verified by the experimental data, and a parametric study was carried out.