Although recombinase polymerase amplification (RPA) has many advantages for the detection of pathogenic nucleic acids in point-of-care applications, RPA has not yet been applied for has not yet been implemented to quantify sample concentration using a standard curve. Here we describe a real-time RPA assay with an internal positive control and an algorithm that analyzes the real-time fluorescence data to quantify HIV-1 DNA. We show that DNA concentration and the onset of detectable amplification are correlated by an exponential standard curve. In a set of experiments in which the standard curve and algorithm were used to analyze and quantify additional DNA samples, the algorithm predicted an average concentration within one order of magnitude of the correct concentration for all HIV-1 DNA concentrations tested. These results suggest that qRPA may serve as a powerful tool for quantifying nucleic acids and may be adapted for use in single-sample point-of-care diagnostic systems.