Graphene-silicon charge-sampling devices (CSD) can achieve remarkable sensitivity to weak light detection, benefiting from intrinsic amplification and nondestructive signal readout, showing vast application prospects. Since the response signal and readout strategy significantly differ from traditional photodetectors, a dedicated readout integrated circuit (ROIC) is essential, specifically designed to be compatible with the nonuniformity of CSDs while ensuring the output with high linearity. Here, we investigate the readout technique and design an efficient dedicated ROIC, which is fabricated in 55-nm mixed-signal CMOS process, tailored to the signal characteristics of CSD. The ROIC operates on the linear relation between graphene channel resistance and illumination intensity, capturing the dynamic changes in the key device parameters. We demonstrate a prototype system comprising ROIC and graphene-silicon CSD. Under near-infrared illumination at 808 nm, the system achieves weak light detection and readout at 573 pW, and exhibits a marginal nonlinearity error of 2% in the readout signal. At a laser intensity of 19.81 nW, the readout channels on the ROIC display a relative standard deviation of 3.41%.