The polarization characteristics of the linear Breit-Wheeler (LBW) pair-production process in polarized $\gamma \gamma$ colliders have been investigated via our developed spin-resolved binary collision simulation method. We find that the 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. We confirm that the polarized $\gamma \gamma$ collider with an asymmetric setup can be performed with currently achievable laser-driven high-density x rays and high-brilliance $\gamma$-photon beams to produce abundant polarized LBW pairs, fulfilling the detection power of polarimetries. Our method and results on the polarized LBW process have plenty of significant applications in strong-field physics, high-energy physics and astrophysics, such as calibrating and monitoring the polarized $\gamma \gamma$ collider and challenging the current understanding of astrophysical objects through enhancing the opacity of $\gamma$-photons to exacerbate the inconsistency between some observations and standard models.