The rule of law is reflected in several constitutional provisions. There are provisions in the Constitution for removing judges, congressmen, and even the President if they misbehave. The House and Senate have to keep a record of what they do so people will know what the laws are that they pass. And the laws must be voted on -- not simply decreed by the President -- so even the President has to ask someone else to change the law. The 14th Amendment says that all citizens should get "equal protection" under the law.
There are some ways in which rule of law is not reflected in the Constitution, too. For example, members of Congress cannot usually be arrested when they are traveling to vote. And the concept of "sovereign immunity" -- that the government cannot be sued without its consent, remains a part of our law.