  A tantalizing hint of isotropic cosmic birefringence has been found in the $E
B$ cross-power spectrum of the cosmic microwave background (CMB) polarization
data with a statistical significance of $3\sigma$. A pseudoscalar field coupled
to the CMB photons via the Chern-Simons term can explain this observation. The
same field may also be responsible for early dark energy (EDE), which
alleviates the so-called Hubble tension. Since the EDE field evolves
significantly during the recombination epoch, the conventional formula that
relates $E B$ to the difference between the $E$- and $B$-mode auto-power
spectra is no longer valid. Solving the Boltzmann equation for polarized
photons and the dynamics of the EDE field consistently, we find that currently
favored parameter space of the EDE model yields a variety of shapes of the $EB$
spectrum, which can be tested by CMB experiments.
