Carbon-based sensors have shown great potential to revolutionize protein diagnostic tools, including the ability to detect pathogens and biomarkers. Many different microdevices have been fabricated using carbon nanotubes and graphene nanoplatelets. However, creating devices on the nanoscale can be difficult and expensive. Stacked graphene nanoparticle composites (hereafter called graphene paper) are a convenient and novel technology that has not been previously reported as a carbon-based sensor platform. Graphene paper is inexpensive and available on a macroscale, making device construction simple. Additional advantages include that paper composition and additives can be manipulated to increase the sensitivity and eventually the selectivity of proteins. We have created a microdevice sensor that detects proteins in solution by measuring the surface electrical resistivity of graphene/cellulose composite paper as a function of protein concentration. Four different proteins were tested for their ability to change the surface resistivity of the graphene paper and there was a clear correlation between the molecular weight of the protein and the equilibrium dissociation constant calculated by fitting the protein adsorption data to the Langmuir isotherm model. This result implies that the dissociation constant is likely a function of the size of the protein.