Catalysis of the transfer of SUMO to a substrate protein via the reaction X-SUMO + S --> X + S-SUMO, where X is either an E2 or E3 enzyme, the X-SUMO linkage is a thioester bond, and the S-SUMO linkage is an isopeptide bond between the C-terminal amino acid of SUMO and the epsilon-amino group of lysine residues in the substrate. (Gene Ontology, GO_0061665)
