Parker was the author of Bibliotheca biblica, or Patristic Commentary on the Scriptures (1720-1735), an abridged translation of Eusebius, and other works. He was also responsible during 1708 and 1709 for a monthly periodical entitled Censura temporum, or Good and Ill Tendencies of Books, which included censure of the religious ideas of Locke and Whiston. Parker was a nonjuror, but he was persuaded by Dodwell's arguments in The Case in View, and began attending the Church of England again circa 1710. However, he continued to avoid taking the oaths. He ran an academy in Oxford (where the nonjuror Thomas Deacon was educated) and provided room and board for visiting foreigners for many years. He had at least five sons. His son Sackville Parker was a well-known Oxford bookseller who was friends with Samuel Johnson. His descendants founded the well-known bookselling establishment in Oxford.

His father was the English theologian and clergyman Samuel Parker (1640-1688) who during the reign of James II served as Bishop of Oxford.