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 Music Branch of the Academy, a candidate must:
(a) have a minimum of three on-screen, theatrical feature film credits (one of the films having been released in the past six years) in which the composing, lyric writing or music editing aspects have achieved distinction and, in the opinion of the Music Branch Executive Committee, reflect the high standards of the Academy,
(b) have a minimum of three on-screen, theatrical feature film credits and, in the view of the executive committee, have made an outstanding musical contribution in the field of theatrical motion pictures,
(the foregoing paragraphs specifically exclude credits for licensed music not written directly for the motion picture in which it receives a screen credit, as well as screen credits for the duties of Music Producer, Music Supervisor, Orchestrator, or Performer)
(c) have been nominated for an Academy Music Award.