Funny that almost no one knows this. But then, schools are so busy rewriting history, who has time to teach what actually happened.
SCOTUS ruled themselves the constitutional interpretation power in the case of Marbury v. Madison, which was decided during the first term of President Thomas Jefferson.
"The question whether the judges are invested with exclusive authority to decide on the constitutionality of a law has been heretofore a subject of consideration with me in the exercise of official duties. Certainly there is not a word in the Constitution which has given that power to them more than to the Executive or Legislative branches." --Thomas Jefferson to W. H. Torrance, 1815. ME 14:303