An enzyme that catalyzes the formation of glycerol 3-phosphate from ATP and glycerol. dihydroxyacetone and L-glyceraldehyde can also act as acceptors; UTP and, in the case of the yeast enzyme, ITP and GTP can act as donors. It provides a way for glycerol derived from fats or glycerides to enter the glycolytic pathway. EC 2.7.1.30.