History does not give an exact date when a Bible what first used to swear or confirm an oath. Paul Boller (a professor on 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.
Its first use
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 to swear upon by a local Masonic Lodge (which has also loaned out the book for other inaugurations).
Washington took his 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.
Other examples
Abraham Lincoln, at his inauguration as president of the United States in 1861, used a copy of God's word to swear upon. 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 Matthew 7:1, 18:7 and Revelation 16:7.
Some presidents have deviated from tradition during their inauguration ceremony. In 1853, Franklin Pierce affirmed, rather than swear, his presidential oath and broke tradition by not kissing the Bible.
Theodore Roosevelt, in 1901 A.D., became the only president not sworn in using a copy of God's word. Harry Truman, in 1945, held a closed copy of Scripture in his left hand, and placed his right hand on the upper cover. Dwight Eisenhower, in 1953, 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, to swear his oath of office. 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 son (Robert Todd Lincoln). Obama is the first president to use this historic volume.
What should Christians do?
In spite of such traditions that swear 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. Jesus taught this principle in his famous Sermon on the Mount.
Again, you have heard that it was said to those in ancient times, 'You shall not forswear yourself, but you shall perform your oaths to the Lord.' But I say to you, do not swear at all, neither by heaven, for it is God's throne; Nor by the earth, for it is the footstool of His feet . . .
But let your word be good, your 'Yes' be yes and your 'No' be no; for anything that is added to these is from the evil one (Matthew 5:33 - 35, 37, HBFV).