Surveillance Order Reporting Act of 2013 - Permits each electronic service provider to report information to the public about requests and demands for information made by any government entity under a surveillance law and exempts such provider from liability with respect to that report even if the provider would otherwise be prohibited by a surveillance law from reporting that information.

Allows the provider to report such information not more often than quarterly and only to the extent that the report reveals estimates of the number of such demands and requests made, the number the service provider complied with, and the numbers of users and/or accounts for which information was demanded, requested, or provided.

Permits any estimate disclosed to be: (1) an overall estimate or broken down by categories of, or provisions of, authorizing surveillance laws; and (2) expressed in no greater detail than in a range of 100, rounded to the nearest 100s.

Defines "surveillance law" to include the Foreign Intelligence Surveillance Act of 1978 and specified sections of the National Security Act of 1947, the Right to Financial Privacy Act of 1978, the Fair Credit Reporting Act, and the federal criminal code (dealing with counterintelligence access to telephone toll and transactional records).