  We provide a new analysis technique to measure the effect of the isotropic
polarization rotation, induced by e.g. the isotropic cosmic birefringence from
axion-like particles and a miscalibration of CMB polarization angle, via mode
coupling in the cosmic microwave background (CMB). Several secondary effects
such as gravitational lensing and CMB optical-depth anisotropies lead to mode
coupling in observed CMB anisotropies, i.e., non-zero off-diagonal elements in
the observed CMB covariance. To derive the mode coupling, however, we usually
assume no parity violation in the observed CMB anisotropies. We first derive a
new contribution to the CMB mode coupling arising from parity violation in
observed CMB. Since the isotropic polarization rotation leads to parity
violation in the observed CMB anisotropies, we then discuss the use of the new
mode coupling for constraining the isotropic polarization angle. We find that
constraints on the isotropic polarization angle by measuring the new
mode-coupling contribution are comparable to that using the $EB$ cross-power
spectrum in future high-sensitivity polarization experiments such as CMB-S4 and
LiteBIRD. Thus, this technique can be used to cross-check results obtained by
the use of the $EB$ cross-power spectrum.
