Understanding the interactions between silicon-based materials and proteins from the bloodstream is of key importance in a myriad of realms, such as the design of nanofluidic devices and functional biomaterials, biosensors, and biomedical molecular diagnosis. By using nanopores fabricated in 20 nm-thin silicon nitride membranes and highly sensitive electrical recordings, we show single-molecule observation of nonspecific protein adsorption onto an inorganic surface. A transmembrane potential was applied across a single nanopore-containing membrane immersed into an electrolyte-filled chamber. Through the current fluctuations measured across the nanopore, we detected long-lived captures of bovine serum albumin (BSA), a major multifunctional protein present in the circulatory system. Based upon single-molecule electrical signatures observed in this work, we judge that the bindings of BSA to the nitride surface occurred in two distinct orientations. With some adaptation and further experimentation, this approach, applied on a parallel array of synthetic nanopores, holds potential for use in methodical quantitative studies of protein adsorption onto inorganic surfaces.