Magnetic anisotropy in strontium iridate (Sr2IrO4) is found to be large because of the strong spin-orbit interactions. In our work, we studied the in-plane magnetic anisotropy of Sr2IrO4 and traced the anisotropic exchange interactions between the isospins in the crystal. The magnetic-field-dependent torque τ(H) showed a prominent transition from the canted antiferromagnetic state to the weak ferromagnetic (WFM) state. A comprehensive analysis was conducted to examine the isotropic and anisotropic regimes and probe the easy magnetization axis along the ab plane. The angle-dependent torque τ(θ) revealed a deviation from the sinusoidal behavior, and small differences in hysteresis were observed around 0° and 90° in the low-magnetic-field regime. This indicates that the orientation of the easy axis of the FM component is along the b axis, where the antiferromagnetic to WFM spin-flop transition occurs. We compared the coefficients of the magnetic susceptibility tensors and captured the anisotropy of the material. The in-plane τ(θ) revealed a tendency toward isotropic behavior for fields with values above the field value of the WFM transition.