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We derive new constraints on axion-like particles (ALPs) using precision
$X$-ray polarization studies of magnetars. Specifically, we use the first
detection of polarized $X$-rays from the magnetars 4U 0142+61 and 1RXS
J170849.0-400910 by the Imaging $X$-ray Polarimetry Explorer (IXPE) to place
bounds on the product of the ALP-photon and ALP-nucleon couplings,
$g_{a\gamma}g_{aN}$, with $g_{aN}$ being responsible for ALP production in the
core of the magnetar and $g_{a\gamma}$ controlling the ALP-photon conversion
probability in the magnetosphere. These bounds are most sensitive to the
magnetar core temperature, and we use two benchmark values of $1\times 10^8$ K
and $5\times 10^8$ K to derive our constraints. For the latter choice, our
bounds are competitive with the existing bounds on the coupling product coming
from a combination of CAST (for $g_{a\gamma}$) and SN1987A (for $g_{aN}$). We
advocate for more precise and extensive observational campaigns in the higher
end of the $2~-~8~$keV spectral window, where ALP-induced polarization is the
strongest. We further advocate for hard $X$-ray polarization studies of young,
hot, near-Earth magnetars with strong magnetic fields.