Single-stranded DNA (ssDNA) regions form as an intermediate in many DNA-associated transactions. Multiple cellular proteins interact with ssDNA via the oligonucleotide/oligosaccharide-binding (OB) fold domain. The heterotrimeric, multi-OB fold domain-containing Replication Protein A (RPA) complex has an essential genome maintenance role, protecting ssDNA regions from nucleolytic degradation and providing a recruitment platform for proteins involved in responses to replication stress and DNA damage. Here, we identify the uncharacterized protein RADX (CXorf57) as an ssDNA-binding factor in human cells. RADX binds ssDNA via an N-terminal OB fold cluster, which mediates its recruitment to sites of replication stress. Deregulation of RADX expression and ssDNA binding leads to enhanced replication fork stalling and degradation, and we provide evidence that a balanced interplay between RADX and RPA ssDNA-binding activities is critical for avoiding these defects. Our findings establish RADX as an important component of cellular pathways that promote DNA replication integrity under basal and stressful conditions by means of multiple ssDNA-binding proteins.