  We point out that the rotation angle $\beta$ of cosmic birefringence, which
is a recently reported parity-violating signal in the cosmic microwave
background (CMB), has a phase ambiguity of $n\pi \,(n\in\mathbb{Z})$. This
ambiguity has a significant impact on the interpretation of the origin of
cosmic birefringence. Assuming an axion-like particle as the origin of cosmic
birefringence, this ambiguity can be partly broken by the anisotropic cosmic
birefringence and the shape of the CMB angular power spectra. We also discuss
constraints on $\beta$ from existing experimental results.
