Exascale Computing for Science, Competitiveness, Advanced Manufacturing, Leadership, and the Economy Act of 2013 or ExaSCALE Computing Leadership Act of 2013 - Renames the Department of Energy High-End Computing Revitalization Act of 2004 as the Exascale Computing for Science, Competitiveness, Advanced Manufacturing, Leadership, and the Economy Act of 2013.

Defines "exascale computing" as computing through the use of a computing machine that performs near or above 10 to the 18th power floating point operations per second.

Directs the Secretary of Energy (DOE) to: (1) conduct a research program to develop exascale computing machines to promote DOE missions; (2) establish national laboratory-industry partnerships for the research and development of exascale computing machines across all applicable DOE agencies; (3) implement the program through an integration of application, computer science, and computer hardware architecture using public-private partnerships to ensure that exascale computing machines are capable of solving DOE target applications and scientific problems; and (4) use existing funds to carry out the program.

Authorizes appropriations for FY2014-FY2016.