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 Film Editors Branch of the Academy, an individual must be approved by a 2/3 majority vote of the Executive Committee and must:
(a) have a minimum of four theatrical feature film credits of a caliber which, in the opinion of the Executive Committee, reflect the high standards of the Academy. These credits must be principal position screen credits as film editor with at least two being single card credits. Shared cards shall count as 1/2 credit. Supervising film editor credits also shall count as 1/2 credit. Every candidate, including those who have edited pictures nominated in the Best Picture, Documentary Feature, Animated Feature Film or Foreign Language Film category, must fulfill these minimum requirements,
(b) have a principal position screen credit as film editor on a picture nominated for Film Editing,
(c) have, in the opinion of the Film Editors Branch Executive Committee, otherwise achieved unique distinction, earned special merit or made an outstanding contribution as a motion picture film editor.
Proposals must be accompanied by a letter from each sponsor which addresses, as specifically as possible, how the candidate meets one or another of the requirements