FISA Court Oversight Underscoring Responsibility and Transparency Act or the FISA COURT Act - Amends the Foreign Intelligence Surveillance Act of 1978 (FISA) to require the Foreign Intelligence Surveillance Court to consist of 11 publicly designated district court judges, of whom:

• 2 judges are designated by the President;
• 1 judge is designated by a majority of the Supreme Court; and
• 2 judges each are designated, respectively, by the Speaker of the House of Representatives, the minority leader of the House of Representatives, and the majority and minority leaders of the Senate.

(Currently, the Chief Justice designates all 11 judges.)

Requires a majority of the Supreme Court (currently, the Chief Justice alone) to designate three judges from the U.S. district courts or courts of appeals who shall comprise the Foreign Intelligence Surveillance Court of Review.

Requires the Attorney General (DOJ) to make publicly available: (1) copies of FISA court decisions, orders, pleadings, applications, and memoranda currently submitted to Congress, subject to the authority of the Attorney General to waive such public availability requirements for national security purposes; and (2) a quarterly estimate of the number of waivers along with the reasons for such waivers.