  Dense positrons are shown to be effectively generated from laser-solid
interactions in the strong-field quantum electrodynamics (QED) regime. Whether
these positrons are polarized has not yet been reported, limiting their
potential applications. Here, by QED particle-in-cell simulations including
electron-positron spin and photon polarization effects, we investigate a
typical laser-solid setup that an ultraintense linearly polarized laser
irradiates a foil target with $\mu$m-scale-length preplasma. We find that once
the positron yield becomes appreciable with the laser intensity exceeding
$10^{24}~\rm W/\rm cm^2$, the positrons are obviously polarized. The polarized
positrons can acquire $>30\%$ polarization degree and $>30$ nC charge with a
flux of $10^{12}\,{\rm sr}^{-1}$. The polarization relies on the deflected
angles and can reach 60\% at some angles and energies. The angularly-dependent
polarization is attributed to the asymmetrical laser fields positrons undergo
in the skin layer of overdense plasma, where the radiative spin-flip and
radiation reaction play significant roles. The positron polarization is robust
and could generally appear in future 100-PW-class laser-solid experiments for
various applications.
