Probing vacuum structures deformed by high intense fields is of great interest in general. In the context of quantum electrodynamics (QED), the vacuum exposed by a linearly polarized high-intensity laser field is expected to show birefringence. We consider the combination of a 10 PW laser system to pump the vacuum and 1 GeV photons to probe the birefringent effect. The vacuum birefringence can be measured via the polarization flip of the probe γ-rays which can also be interpreted as phase retardation of probe photons. We provide theoretically how to extract phase retardation of GeV probe photons via pairwise topology of the Bethe-Heitler process in a polarimeter and then evaluate the measurability of the vacuum birefringence via phase retardation given a concrete polarimeter design with a realistic set of laser parameters and achievable pulse statistics.