Sickle cell disease (SCD) is a group of common, life-threatening disorders caused by a point mutation in the β globin gene. Early diagnosis through newborn and early childhood screening, parental education, and preventive treatments are known to reduce mortality. However, the cost and complexity of conventional diagnostic methods limit the feasibility of early diagnosis for SCD in resource-limited areas worldwide. Although several point-of-care tests are commercially available, most are antibody-based tests, which cannot be used in patients who have recently received a blood transfusion. Here, we describe the development of a rapid, low-cost nucleic acid test that uses real-time fluorescence to detect the point mutation encoding hemoglobin S (HbS) in one round of isothermal recombinase polymerase amplification (RPA). When tested with a set of clinical samples from SCD patients and healthy volunteers, our assay demonstrated 100% sensitivity for both the βA globin and βS globin alleles and 94.7 and 97.1% specificities for the βA globin allele and βS globin allele, respectively (n = 91). Finally, we demonstrate proof-of-concept sample-to-answer genotyping of genomic DNA from capillary blood using an alkaline lysis procedure and direct input of diluted lysate into RPA. The workflow is performed in <30 min at a cost of <$5 USD on a commercially available benchtop fluorimeter and an open-source miniature fluorimeter. This study demonstrates the potential utility of a rapid, sample-to-answer nucleic acid test for SCD that may be implemented near the point of care and could be adapted to other disease-causing point mutations in genomic DNA.