  How to measure the optical conductivity of atomically thin crystals is an
important but challenging issue due to the weak light-matter interaction at the
atomic scale. Photonic spin Hall effect, as a fundamental physical effect in
light-matter interaction, is extremely sensitive to the optical conductivity of
atomically thin crystals. Here, we report a precision measurement of the
optical conductivity of graphene, where the photonic spin Hall effect acts as a
measurement pointer. By incorporating with the weak-value amplification
technique, the optical conductivity of monolayer graphene taken as a universal
constant of $(0.993\pm0.005)\sigma_0$ is detected, and a high measuring
resolution with $1.5\times10^{-8}\Omega^{-1}$ is obtained. For few-layer
graphene without twist, we find that the conductivities increase linearly with
layer number. Our idea could provide an important measurement technique for
probing other parameters of atomically thin crystals, such as magneto-optical
constant, circular dichroism, and optical nonlinear coefficient.
