Americans do not have a right to privacy that is specifically spelled out anywhere in the Constitution. There is no part of the Constitution that actually says that there is such a right. However, courts have ruled that the Constitution implies that there is a right to privacy.
What courts have rules is that the various protections in the Constitution add up to a general rule that we have a right to privacy. We are explicitly protected from searches and seizures without a warrant. We are explicitly given the right to have whatever political and religious beliefs we want. We are given the right to keep any knowledge we have about crimes we have committed private. Because of explicit protections like these, courts have ruled that the Constitution implies that we do have a right to privacy. The idea is that there are things that are off-limits to government because we live in a democratic system with a limited government.