  Axion-like particles (ALPs) can form a network of cosmic strings and domain
walls that survives after recombination and leads to anisotropic birefringence
of the cosmic microwave background (CMB). In addition to studying cosmic
strings, we clarify and emphasize how the formation of ALP-field domain walls
impacts the cosmic birefringence signal; these observations provide a unique
way of probing ALPs with masses in the range $3H_0 \lesssim m_a \lesssim
3H_{\rm cmb}$. Using measurements of CMB birefringence from several telescopes,
we find no evidence for axion-defect-induced anisotropic birefringence of the
CMB. We extract constraints on the model parameters that include the ALP mass
$m_a$, ALP-photon coupling $\mathcal{A} \propto g_{a\gamma\gamma} f_a$, the
domain wall number $N_{\rm dw}$, and parameters characterizing the abundance
and size of defects in the string-wall network. Considering also recent
evidence for isotropic CMB birefringence, we find it difficult to accommodate
this with the non-detection of anisotropic birefringence under the assumption
that the signal is generated by an ALP defect network.
