Vortex-induced vibration (VIV) is a significant concern when designing slender structures with square cross sections. VIV strongly depends on structural dynamics and flow states, which depend on the conditions of the approaching flow and shape of a structure. Therefore, the effects of the angle of attack on the coupling effects of VIV for a square cylinder are expected to be significant in practice. In this study, the aerodynamic forces for a fixed and elastically mounted square cylinder were measured using wind pressure tests. Aerodynamic forces on the stationary cylinder are firstly discussed by comparisons of variation of statistical aerodynamic force and wind pressure coefficient with wind angle of attack. The coupling effect between the aerodynamic forces and the motion of the oscillating square cylinder by VIV is subsequently investigated in detail at typical wind angels of attack with occurrence of three typical flow regimes, i.e., leading-edge separation, separation bubble (reattachment), and attached flow. The coupling effect are illustrated by discussing the onset of VIV, characteristics of aerodynamic forces during VIV, and interaction between motion and aerodynamic forces. The results demonstrate that flow states can be classified based on final separation points or the occurrence of reattachment. These states significantly influence coupling effects of the oscillating cylinder. Vibration enhances vortex shedding, which creates strong fluctuations in aerodynamic forces. However, differences in the lock-in range, aerodynamic force, and interaction process for angles of attack smaller and larger than the critical angle of attack revealed noteworthy characteristics in the VIV of a square cylinder.