Deference to the Bluebook
While APA style includes rules for the citation of government publications, there is no specific entry for constitutions included in the sixth edition (second printing) of the Publication Manual of the American Psychological Association. In this case, APA style defers to The Bluebook: A Uniform System of Citation, which sets the bar for legal citations. The Bluebook is described as the nation's definitive legal citation style guide and is used by lawyers and judges, as well as scholars and law students.
Making the Citation
If you make a brief reference to the U.S. Constitution, there is no need to actually cite it. However, if you are using a specific section of the document, such as the Second Amendment, to back up your argument, you are required to cite it. According to the 19th edition of The Bluebook, all references to the U.S. Constitution should begin "U.S. Const." Following that, include the relevant section -- in this case, the Second Amendment, which would be identified as "amend. II."
The Final Product
Ultimately, your final citation will read like this: U.S. Const. amend. II. The reference is the same whether used as an in-text citation or in a reference list at the conclusion of the document.