The process in which a relatively unspecialized cell acquires the specialized structural and/or functional features of a pericardial nephrocyte. A pericardial nephrocyte is an insect renal cell that filters hemolymph and is found with other pericardial nephrocytes in two rows flanking the dorsal vessel. Differentiation includes the processes involved in commitment of a cell to a specific fate and its subsequent development to the mature state.