Final answer:
Dorothy Arzner was the first woman to join the Directors Guild of America in the early 1930s, becoming a pioneering female director in Hollywood's Golden Age.
Step-by-step explanation:
The first woman to join the Directors Guild of America was Dorothy Arzner in the early 1930s. Arzner was a pioneering director during Hollywood's Golden Age and became the first woman to direct a sound film. She was recognized for her contributions to film and her trailblazing role as a woman in a male-dominated industry. While the provided reference materials do not contain information on Dorothy Arzner, historical records confirm her status as the first woman member of the Directors Guild of America.