Bioactive, electrospun polymer nanofibers (NFs) are attractive building-block materials for realizing scaffolds for tissue engineering, as these filaments structurally mimic the hierarchical organization of natural extracellular matrix. As presented in this article, demonstrated applications involve the commitment to adipogenic, chondrogenic, osteogenic, neural lineages, and so on, by different types of stem cells obtained from various sources (adult, embryonic, induced pluripotent stem cells, etc.). Since a poor cellular colonization may limit the usefulness of scaffolds for culturing delicate stem cell populations, coupling NFs with cell-adhesive domains is highly desirable. In our work, the surface of either isotropic (randomly oriented) or anisotropic (highly aligned) electrospun poly(L-lactic acid) fibrous scaffolds with fibronectin (FN)-mimetic peptides is tailored. The effects of the peptide immobilization on the adhesion and spreading of human, adult renal stem cells are investigated. Functionalized, aligned NFs are suitable scaffolds to promote the confluent growth of stem cells and to enhance their differentiation toward the tubular epithelial lineage. It is anticipated that the functionalization of aligned NFs with FN-mimetic peptides might be a promising method to target a specific response of stem cells in renal tissue engineering.