Restoring Integrity to America's Elections Act This bill amends the Federal Election Campaign Act of 1971 with respect to the Federal Election Commission (FEC) to: (1) reduce the number of members of the FEC from eight to five, (2) remove the Secretary of the Senate and Clerk of the House as ex officio members, and (3) permit no more than two members to be affiliated with the same political party. A majority of the FEC members serving at the time shall constitute a quorum, except that three shall constitute a quorum if there are only four members serving. A Blue Ribbon Advisory Panel shall recommend to the President individuals for nomination to the FEC. The President shall appoint the FEC Chair, subject to Senate confirmation as a member of the FEC. The powers of the FEC are revised and distributed between the chair and the other FEC members. Persons who submit written comments regarding requests for advisory opinions must be given an opportunity to appear at FEC hearings on such requests.