  Laser-driven brilliant controllable polarized $\gamma$-photon sources open
the way for designing compact $\gamma\gamma$ collider, which enable the large
yield of linear Breit-Wheeler (LBW) pairs in a single shot and thus provide an
opportunity for the investigation of polarized LBW process. In this work we
investigate the polarization characteristics of LBW pair production via our
developed spin-resolved binary collision simulation method. Polarization of
$\gamma$-photons modifies the kinematics of scattering particles and induces
the correlated energy-angle shift of LBW pairs, and the latter's polarization
characteristic depends on the helicity configures of scattering particles. Our
method confirms that the polarized $\gamma\gamma$ collider with an asymmetric
setup can be performed with currently achievable laser facilities to produce
abundant polarized LBW pairs, fulfilling the detection power of polarimetries.
The precise knowledge of polarized LBW process is in favor of the calibration
and monitor of polarized $\gamma\gamma$ collider, and could enhance the opacity
of $\gamma$-photons in high-energy astrophysical objects to exacerbate the
inconsistency between some observations and standard models.
