Twisted bilayer graphene (TBG) exhibits many fascinating electronic and transport properties. Here we analyze the nonlinear optical response in TBG in the terahertz regime. By considering an effective two-band model with a simplified interlayer tunnel, we write the time-dependent wave function in terms of generalized Floquet states consisting of multiple high-order harmonics. A two-component spinor recursion relation is solved up to terms in the third order of the applied field. The third-order conductivity of TBG with different twist angles is obtained. For small twist angles the Kerr effect dominates over the high harmonic processes, while for large twist angles, the high harmonic processes completely dominate the nonlinear response. We attribute this phenomenon to the band dispersion sensitive transition probability in low- and high-energy regimes. The frequency- and temperature-dependent critical field is also presented. The critical field is insensitive to the temperature, indicating that the nonlinear response persists at room temperature.