We demonstrate a handheld on-chip biosensing technology that employs plasmonic microarrays coupled with a lens-free computational imaging system towards multiplexed and high-throughput screening of biomolecular interactions for point-of-care applications and resource-limited settings. This lightweight and field-portable biosensing device, weighing 60 g and 7.5 cm tall, utilizes a compact optoelectronic sensor array to record the diffraction patterns of plasmonic nanostructures under uniform illumination by a single-light emitting diode tuned to the plasmonic mode of the nanoapertures. Employing a sensitive plasmonic array design that is combined with lens-free computational imaging, we demonstrate label-free and quantitative detection of biomolecules with a protein layer thickness down to 3 nm. Integrating large-scale plasmonic microarrays, our on-chip imaging platform enables simultaneous detection of protein mono- and bilayers on the same platform over a wide range of biomolecule concentrations. In this handheld device, we also employ an iterative phase retrieval-based image reconstruction method, which offers the ability to digitally image a highly multiplexed array of sensors on the same plasmonic chip, making this approach especially suitable for high-throughput diagnostic applications in field settings.