We propose an ultra-low-cost at-home blood pressure monitor that leverages a plastic clip with a spring-loaded mechanism to enable a smartphone with a flash LED and camera to measure blood pressure. Our system, called BPClip, is based on the scientific premise of measuring oscillometry at the fingertip to measure blood pressure. To enable a smartphone to measure the pressure applied to the digital artery, a moveable pinhole projection moves closer to the camera as the user presses down on the clip with increased force. As a user presses on the device with increased force, the spring-loaded mechanism compresses. The size of the pinhole thus encodes the pressure applied to the finger. In conjunction, the brightness fluctuation of the pinhole projection correlates to the arterial pulse amplitude. By capturing the size and brightness of the pinhole projection with the built-in camera, the smartphone can measure a user's blood pressure with only a low-cost, plastic clip and an app. Unlike prior approaches, this system does not require a blood pressure cuff measurement for a user-specific calibration compared to pulse transit time and pulse wave analysis based blood pressure monitoring solutions. Our solution also does not require specialized smartphone models with custom sensors. Our early feasibility finding demonstrates that in a validation study with N = 29 participants with systolic blood pressures ranging from 88 to 157 mmHg, the BPClip system can achieve a mean absolute error of 8.72 and 5.49 for systolic and diastolic blood pressure, respectively. In an estimated cost projection study, we demonstrate that in small-batch manufacturing of 1000 units, the material cost is an estimated $0.80, suggesting that at full-scale production, our proposed BPClip concept can be produced at very low cost compared to existing cuff-based monitors for at-home blood pressure management.