The Constitution does not specifically set out the power of judicial review. However, it at least implies that the power exists. The Supreme Court formally took that power for itself in the 1803 case of Marbury v. Madison.
The Constitution does say, in Article 6, Clause 2, that it is the supreme law of the land. That implies that all laws have to conform to the Constitution and that a law is void if it does not. In Article Two, the Constitution says that “the judicial power of the United States, shall be vested in one Supreme Court” and that the judicial power includes “all cases, in law and equity, arising under this Constitution.” This implies that all cases having to do with the Constitution will be heard by the federal courts. However, the Constitution never explicitly says anything like “The Supreme Court shall have the power to invalidate laws if it holds that the laws violate the Constitution.”
The power to do this was actually taken by the Supreme Court in 1803. In that case, the Court declared that a law passed by Congress could not be enforced because it was contrary to the Constitution. It declared that it had the power to make this determination. Although the Constitution did not explicitly give the Supreme Court this power, it is plausible to infer that the Court should have the power of judicial review.