Refractive error is the most common eye disorder and is the key cause behind correctable visual impairment, responsible for nearly 80% of the visual impairment in the US. Refractive error can be diagnosed using multiple methods, including subjective refraction, retinoscopy, and autorefractors. Although subjective refraction is the gold standard, it requires cooperation from the patient and hence is not suitable for infants, young children, and developmentally delayed adults. Retinoscopy is an objective refraction method that does not require any input from the patient. However, retinoscopy requires a lens kit and a trained examiner, which limits its use for mass screening. In this work, we automate retinoscopy by attaching a smartphone to a retinoscope and recording retinoscopic videos with the patient wearing a custom pair of paper frames. We develop a video processing pipeline that takes retinoscopic videos as input and estimates the net refractive error based on our proposed extension of the retinoscopy mathematical model. Our system alleviates the need for a lens kit and can be performed by an untrained examiner. In a clinical trial with 185 eyes, we achieved a sensitivity of 91.0% and specificity of 74.0% on refractive error diagnosis. Moreover, the mean absolute error of our approach was 0.75$\pm$0.67D on net refractive error estimation compared to subjective refraction measurements. Our results indicate that our approach has the potential to be used as a retinoscopy-based refractive error screening tool in real-world medical settings.