We propose a way to use room temperature random telegraph noise to characterize single molecules adsorbed on a backgated silicon field-effect transistor. The overlap of molecule and silicon electronic wave functions generates a set of trap levels that impose their unique scattering signatures on the voltage-dependent current noise spectrum. Our results are based on numerical modeling of the current noise, obtained by coupling a density functional treatment of the trap placement within the silicon band gap, a quantum kinetic treatment of the output current, and a Monte Carlo evaluation of the trap occupancy under resonance. As an illustrative example, we show how we can extract molecule-specific "fingerprints" of four benzene-based molecules directly from a frequency-voltage colormap of the noise statistics. We argue that such a colormap carries detailed information about the trap dynamics at the Fermi energy, including the presence of correlated interactions, observed experimentally in backgated carbon nanotubes.