We demonstrate that linear absorption coefficient (LAC) of a graphene-silicon hybrid waveguide (GSHW) is determined by the optical transmission spectra of a graphene coated symmetrically coupled add-drop silicon microring resonator (SC-ADSMR), of which the value is around 0.23 dB/um. In contrast to the traditional cut-back method, the measured results are not dependent on the coupling efficiency of the fiber tip and the waveguide. Moreover, precision evaluation of graphene coated silicon microring resonator (SMR) is crucial for the optoelectronic devices targeting for compact footprint and low power consumption.