It's not an absolute right, but certain aspects one's privacy are protected by the fourth amendment.
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
Of course the right is very limited. A reasonable search is permitted, but requires a warrant under most circumstances. IMHO, a search with a warrant is not reasonable if the warrant is served in an unreasonable manner, or if the warrant does not meet the requirement to be particular (that is specific to the individual case, blanket warrants are not allowed). A "defective" warrant that fails to indicate probable cause would also result in an unreasonable search.
Clearly this isn't what was meant by privacy right. We know what the 4th amendment says. He's talking about the invention of a privacy right, but the Warren Court, to justify the Court's imposition of a radical cultural agenda, such as abortion on demand, etc.