Pinpointing functional noncoding DNA sequences and defining their contributions to health-related traits is a major challenge for modern genetics. We developed a high-throughput framework to map noncoding DNA functions with single-nucleotide resolution in four loci that control erythroid fetal hemoglobin (HbF) expression, a genetically determined trait that modifies sickle cell disease (SCD) phenotypes. Specifically, we used the adenine base editor ABEmax to introduce 10,156 separate A•T to G•C conversions in 307 predicted regulatory elements and quantified the effects on erythroid HbF expression. We identified numerous regulatory elements, defined their epigenomic structures and linked them to low-frequency variants associated with HbF expression in an SCD cohort. Targeting a newly discovered γ-globin gene repressor element in SCD donor CD34+ hematopoietic progenitors raised HbF levels in the erythroid progeny, inhibiting hypoxia-induced sickling. Our findings reveal previously unappreciated genetic complexities of HbF regulation and provide potentially therapeutic insights into SCD.