Synthesizes alpha-1,4-glucan chains using ADP-glucose. [(1->4)-alpha-D-glucosyl](n) + ADP-alpha-D-glucose = [(1->4)-alpha-D-glucosyl](n+1) + ADP + H(+) Glycan biosynthesis; glycogen biosynthesis. Belongs to the glycosyltransferase 1 family. Bacterial/plant glycogen synthase subfamily.