The American Psychological Association Publication Manual provides style and formatting guidelines for the behavioral and social sciences. However, the manual does not specifically deal with legal documents, such as the Bill of Rights from the U.S. Constitution. Instead, APA style uses information from "The Bluebook: A Uniform System of Citation" when such documents are involved.
When you use information about the Bill of Rights in your paper, the U.S. Constitution would be cited within the text. After the information, the citation is placed within parentheses. First, the Constitution is abbreviated "U.S. Const." Then denote "amend." for "amendment" and the Roman numeral of the amendment, such as (U.S. Const. amend. II). If the amendment has since been repealed, the date of the repeal is included inside the parentheses.
If there is an in-text citation of the Bill of Rights, it must also be listed on the reference page at the end. This reference is unlike most APA references. It is listed exactly like the in-text citation with a period at the end. Therefore, the reference page might have an entry such as: U.S. Const. amend. VI.