English Language Unity Act of 2013 - Makes English the official language of the United States.

Requires, subject to exceptions and rules of construction, that: (1) official functions of the U.S. government be conducted in English, and (2) all naturalization ceremonies be conducted in English.

Establishes a uniform English language rule for naturalization.

Makes English language requirements and workplace policies, whether in the public or private sector, presumptively consistent with the laws of the United States.

Directs the Secretary of Homeland Security (DHS) to issue for public notice and comment a proposed rule for uniform testing of English language ability of candidates for naturalization based upon the principles that: (1) all citizens should be able to read and understand generally the English language text of the Declaration of Independence, the Constitution, and the laws of the United States; and (2) any exceptions to this standard should be limited to extraordinary circumstances, such as asylum.