District of Columbia Budget Autonomy Act of 2013 - Amends the District of Columbia Home Rule Act to eliminate, with respect to each fiscal year that is not a control year, all federally-imposed mandates over the District of Columbia's: (1) local budget process, financial management, audits, and accountability requirements; and (2) short-term borrowing of money, with specified exceptions.

Declares that the process by which the District develops and enacts the District government's budget for a fiscal year, the activities carried out regarding financial management of the District government, and the process and rules by which the District issues bonds or otherwise borrows money shall be established under laws enacted by the District.

Provides that Acts adopting the District government's annual budget for FY2014 and succeeding non-control fiscal years shall take effect upon their prescribed dates. (Thus eliminates congressional review of such Acts).

Repeals the federal cap on amounts the District may borrow (other than in a control year).

Repeals the application of the Federal Anti-Deficiency Act to the District government. Makes conforming amendments to the Act.

Makes conforming amendments to the Financial Services and General Government Appropriations Act, 2009.