Architect of the Capitol Appointment Act of 2023 This bill modifies the procedures for appointing and removing the Architect of the Capitol (who is responsible for the operation and care of the Capitol grounds, facilities, and art). Specifically, the bill establishes a bipartisan congressional commission to, by majority vote, appoint, reappoint, and remove the Architect. (Currently, the Architect is appointed by the President and confirmed by the Senate.) The bill also provides for the Deputy Architect to serve as acting Architect in the event the Architect is absent, disabled, or otherwise unavailable. If the Architect fails to appoint a Deputy Architect within a set time frame, the commission must do so. Additionally, in the event of vacancies in both the Architect and Deputy Architect positions, the commission must appoint an acting Architect.