ANSWER: History does not give an exact date when swearing on the Bible in order to confirm an oath first began. Paul Boller (a history professor who has written many books about American politics) states that this practice is it at least two hundred years old, with Christians, non-Christians, and even Jews performing this act. There is some interesting information regarding this practice, however, as it relates to the presidents of the United States.
Although it is not mandated in the U.S. Constitution, it has been customary for a copy of Scripture to be used in swearing in a new president since George Washington first took his oath in 1789. Information from the Architect of the Capitol, plus other resources, reveals that Washington’s inauguration ceremony was planned to the tiniest detail, with one exception. As he prepared to step onto the balcony, someone realized there was no copy of Scripture on hand. A 1767 King James translation was loaned for the occasion by the St John’s Lodge No. 1 of the Masons (which has also loaned out the book for several other presidential inaugurations).
Washington took the swearing in of the oath of office (written for the occasion) after God's word was opened randomly to the book of Genesis, chapter 49, verse 13. He then ad-libbed the phrase 'I solemnly swear, so help me God.' He then kissed the Bible, setting the precedent for other presidents to do the same.
Abraham Lincoln, at his inauguration as president of the United States in 1861, used a copy of God's word for his swearing in ceremony. He randomly opened it and used whatever page was open in order to take the oath of office. In 1865, however, he consciously chose to take his oath upon the following Scriptures.
Judge not, that ye be not judged (Matthew 7:1, KJV)
Woe unto the world because of offences . . . (Matthew 18:7)
Even so, Lord God Almighty, true and righteous are thy judgments (Revelation 16:7)
Some presidents have deviated from tradition during their swearing in ceremony. In 1853, Franklin Pierce affirmed, rather than swore, his presidential oath and broke tradition by not kissing the Bible. In 1901, Theodore Roosevelt became the only president not sworn in using a copy of God's word. In 1945, Harry Truman held a closed copy of Scripture in his left hand, and placed his right hand on the upper cover. In 1953, Dwight Eisenhower recited an improvised prayer rather than kissing the Scriptures.
John F. Kennedy used his family’s Douay translation, brought by his Fitzgerald ancestors from Ireland, for his swearing in oath. Bill Clinton used a King James translation given to him by his grandmother. On January 20, 2009, Barack Obama took his oath of office on the same Bible Abraham Lincoln used to take his. The book was donated in 1928 to the Library of Congress by the widow of Lincoln’s child, Robert Todd Lincoln. Obama is the first president to use this historic volume.
In spite of such traditions that use swearing on the Bible to confirm an oath, Christians are commanded to have a good enough character so that their promise to fulfill what is asked of them is all that is needed (Matthew 5: 33 - 37).