From Academy Bylaws:
Article III, Section 1. Membership shall be by invitation of the Board of Governors. Invitations to active membership shall be limited to those persons active in the motion picture arts and sciences, or credited with screen achievements, or who have otherwise achieved distinction in the motion picture arts and sciences and who, in the opinion of the Board, are qualified for membership.
To be considered for invitation to membership in the Writers Branch of the Academy, an individual must:
(a) have at least two theatrical feature film credits of a caliber which, in the opinion of the executive committee, reflect the high standards of the Academy. Credits should be inclusive of all film genres, and can be films released theatrically, in addition to streaming services and/or screened at a major film festival,
(b) have been nominated for an Academy Writing Award, and/or have a writing credit on a film nominated for the Academy Best Picture Award, Best International Feature Film Award, or Best Animated Feature Film Award,
(c) have, in the judgment of the Writers Branch Executive Committee, otherwise achieved unique distinction, earned special merit or made an outstanding contribution as a motion picture writer.