If the USA actually kept their word, they would already be recognizing it.

Universal Declaration of Human Rights Article 12 states:

No one shall be subjected to arbitrary interference with his privacy, family, home or correspondence, nor to attacks upon his honour and reputation. Everyone has the right to the protection of the law against such interference or attacks.

USA voted in favor of the declaration and the original drafting committee was chaired be Eleanor Reoosevelt.

Most signatories have worked it into their constitituon, but america being america has not done it. They have some references to the human rights declaration in their laws, but nothing regarding privacy. And in fact the US supreme court has ruled that the federal governement can basically choose to ignore it at will.