Congress originally designated March 4 as Inauguration Day, in part to give officials adequate time to tally election returns, and adoption of the Twelfth Amendment made that date part of the U.S. Constitution.
(In fact, George Washington’s first inaugural did not take place until April 30, as inclement weather hampered completion of the official vote count.)
In 1933, adoption of the 20th Amendment to the U.S. Constitution changed Inauguration Day to January 20.
Franklin D. Roosevelt’s first Inaugural took place on March 4, 1933; his second took place, following the adoption of the 20th Amendment, on January 20, 1937. Thus, FDR was the first U.S. President to be inaugurated on the 20th of January.