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The spin-orbit coupled Mott insulator Sr₂IrO₄ has attracted considerable attention because of its exotic J_eff=1/2 Mott state arising from the interplay of on-site Coulomb repulsion and strong spin-orbit coupling. It is of interest to investigate how the magnetization dynamically evolves in response to electromagnetic excitation. We measured the dynamic properties of the J_eff=1/2 Mott state using strong sub-gap excitation (THz and mid-IR), monitoring the induced Kerr signal. THz-induced Kerr rotation is observed below T_N (230K), following the THz pulse shape. Notably, for mid-IR circularly polarized excitation, we observe a strong temperature dependent Kerr rotation below 100K. We will discuss the possible origin of the observed dynamics in this intriguing material.