A comprehensive theoretical study on the low-energy electronic states of the superoxide anion (O ^- ₂) is presented, focusing on the effects of spin-orbit coupling (SOC) on these states. Utilizing the complete active space self-consistent field (CASSCF) method combined with the multireference configuration interaction method with Davidson correction (MRCI+Q), and employing the aug-cc-pV5Z-dk basis set that includes Douglas-Kroll relativistic corrections, electron correlation and relativistic effects are accurately considered. The research concentrates on the first and second dissociation limits of O ^- ₂, calculating the potential energy curves (PECs) and spectroscopic constants of 42 Λ-S states. After introducing SOC, 84 Ω states are obtained through splitting, and their PECs and spectroscopic constants are calculated. Detailed data on the electronic states related to the second dissociation limit are provided for the first time. The results show excellent agreement with existing literature, validating the reliability of the methodology. For the first time, this study confirms through calculations with different basis sets that the double-well structure of the a ⁴Σ ^- _ustate originates from an avoided crossing with the 2 ⁴Σ ^- _ustate, and finds that the size of the basis set significantly affects the depth of its potential wells. After considering SOC, the total energy of the system decreases, especially for states with high orbital angular momentum (such as the 1²Φ _uand 1⁴Δ _gstates), leading to energy level splitting and energy reduction, while other spectroscopic constants remain essentially unchanged. These findings provide valuable theoretical insights into the electronic structure and spectroscopic properties of O ^- ₂, offering important reference data for future research in fields such as atmospheric chemistry, plasma physics, and molecular spectroscopy. The datasets presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00213.00076.