  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.
