Recent theoretical work predicted emergence of chiral topological superconducting phase with spontaneously broken time reversal symmetry in a twisted bilayer composed of two high-$T_c$ cuprate monolayers, such as Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$. Here we identify large intrinsic Hall response that can be probed through the polar Kerr effect measurement as a convenient signature of the $mathcal{T}$-broken phase. Our modelling predicts the Kerr angle $theta_K$ to be in the range of 10-100 $mu$rad, which is a factor of $10^3-10^4$ times larger than what is expected for the leading chiral supercondutor candidate Sr$_2$RuO$_4$. In addition we show that the optical Hall conductivity $sigma_H(omega)$ can be used to distinguish between the topological $d_{x^2-y^2}pm id_{xy}$ phase and the $d_{x^2-y^2}pm is$ phase which is also expected to be present in the phase diagram but is topologically trivial.
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