FISA Court Accountability 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 3 judges are designated by the Chief Justice 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 any authority exercised by the court en banc (consisting of all judges who constitute the court when an en banc proceeding is ordered by a majority of the judges in certain circumstances) to be exercised only when agreed to by at least 60% of the judges sitting en banc.

Directs the Chief Justice, the Speaker, and the majority leader of the Senate (or, if the majority leader is a member of the same political party as the Speaker, the minority leader of the Senate) to each publicly designate one judge from the U.S. district courts or courts of appeals who together shall comprise the Foreign Intelligence Surveillance Court of Review. (Currently, the Chief Justice designates all three of such judges.) Allows such court to decide in favor of the government only if the decision of the reviewing judges is unanimous.

Directs the Attorney General (DOJ) to submit to Congress a copy of any decision, order, or opinion issued by each court (currently, only those issuances with a significant construction or interpretation of FISA) along with an unclassified summary of each such decision, order, or opinion.