Interactions between charged macromolecules (e.g. proteins, polypeptides, nucleic acids) and charged surfaces govern many natural and industrial processes. We investigate here the influence of an applied electric potential on the adsorption of charged polymers, and report the following significant result: the adsorption of certain basic poly(amino acids) may become continuous, i.e. asymptotically linear (or nearly linear) in time over hours, upon the application of a modest anodic potential. Employing optical waveguide lightmode spectroscopy (OWLS) and an indium tin oxide (ITO) substrate, we show asymptotic kinetics – and the adsorbed mass at the onset of the asymptotic regime – to depend sensitively on polymer chemistry (in particular, side chain volume), to increase with applied potential and ionic strength (conditions favoring a thicker initial layer), and to be independent of bulk polymer concentration (suggesting post-adsorption events to be rate limiting). X-ray photoelectron spectra reveal a suppressed average polymer charge within layers formed via continuous adsorption, but no evidence of electrochemical reactions. Atomic force microscopy images reveal the presence of discrete particles of size 2-3 times the polymer hydrodynamic diameter. We propose a mechanism involving post-adsorption conformational re-arrangements, enabled by interfacial conditions favoring weakly charged and strongly charge screened polymers, leading to free surface space upon which additional adsorption may occur. Continuous adsorption under an applied electric potential offers the possibility of polypeptide films of tailored nanoscale thickness realized in a single step.