No. Not the one taking place today. This one is much older (160 years to be precise):
And, in 1857, the first known photograph of a Presidential Inauguration was captured.
This image, seen above, was taken by John Wood, who worked for the Architect of the Capitol under Montgomery C. Meigs. According to a presentation given by Wayne Firth (retired Senior photographer at the Architect of the Capitol) in 1996 at the National Building Museum at the U.S. Capitol, Meigs, who was in charge of the construction of the Capitol at the time, hired Wood as a “photographic draftsman” for the building of the Capitol. His job was to photograph the drawings of the construction so they could be easily duplicated.
During Wood’s tenure at the Capitol, his job grew. And, when Meigs was put in charge of constructing a platform for the Inauguration ceremony, he also constructed a platform for Wood to set up his camera and photograph the inauguration of James Buchanan on March 4, 1857.
Photographer Wood would eventually leave his post at the Architect of the Capitol and go on to photograph in the Civil War. According to the Library of Congress, Wood worked for the Architect of the Capitol from 1856 to 1861 and then moved onto photographing maps in the war for Gen. George McClellan.
Little is known of his later life and works, but his legacy will live on forever with this photo.
Source: This is the first known photography ever taken at a presidential inauguration.