Educated at Harrow, Brasenose College, Oxford, and Göttingen, he was elected fellow of Brasenose and in 1884 keeper of the Ashmolean Museum at Oxford, holding this post till 1908.
He presented to the Ashmolean museum, Oxford, a variety of fossils and antiquities, which he had described in his works, and received the thanks of the university and the degree of LL.D.
These ' Parker's invaluable series of Roman photographs may be seen at the library of the Victoria and Albert museum, at the Ashmolean museum and the Bodleian library, Oxford.
In 1837 he visited the United States, and acquired there the materials for papers on the thermal springs and the geology of North America, read in 1838 before the Ashmolean Society and the British Association.
See Obituary by John Phillips in Proceedings of Ashmolean Soc., 1868.