It is not possible to answer precisely the question 'who was the first woman graduate?' Before October 1920, women were not allowed to matriculate (ie be admitted to become members of the University) or to graduate. From the late 1870s, women had attended lectures, taken examinations, and had gained honours in those examinations. They were, however, unable to receive the degree to which, had they been men, their examinations would have entitled them.
The new University statute of 1920 which admitted women to full membership of the University, and which came into effect from October that year, enabled women who had previously taken, and gained honours in, University examinations to return to matriculate (ie go through the formal ceremony of admission to the University) and have the degree to which they were now entitled conferred on them (again, at a formal ceremony). Consequently, at the very first ceremony at which women were able to graduate more than forty women did so.
The first woman to gain honours in a University examination which was intended to be equivalent to that taken by men for a degree was Annie Mary Anne Henley Rogers. In 1877 she gained first class honours in Latin and Greek in the Second Examination for Honours in the recently instituted 'Examinations for Women'. In 1879 she followed this with first class honours in Ancient History. Annie Rogers matriculated and graduated on 26 October 1920.
Oxford University Archives 2018