As to raising a hand; or placing hand under thigh. In making an oath, it was customary to raise the right hand. God speaks of himself as doing this, symbolically. (De 32:40; Isaiah 62:8) The angel in Daniel’s vision raised both his right hand and his left to heaven to utter an oath. (Daniel 12:7) Another method of confirming an oath was to place one’s hand under the other’s thigh (hip), as Abraham’s steward did in swearing that he would get a wife for Isaac from Abraham’s relatives (Genesis 24:2, 9), and as Joseph did for Jacob in swearing not to bury Jacob in Egypt. (Genesis 47:29-31) The word “thigh” applies to the upper part of the leg from the hip to the knee, in which the femur is located. According to the Jewish rabbi Rashbam, this method of swearing was used when a superior adjured an inferior, such as a master his servant or a father his son, who also owes him obedience. And according to another Jewish scholar, Abraham Ibn Ezra, it was the custom in those days for a servant to take an oath in this manner, placing his hand under his master’s thigh, the latter sitting upon his hand. This signified that the servant was under his master’s authority Source.—The Soncino Chumash, edited by A. Cohen, London, 1956, p. 122. and the scriptures cited – please look them up in your own Bible. This was a good question.

I would also like to add to Perryman's excellent answer. It is also thought that the custom referred to here came about because of the vulnerable position in which it placed the men. This vulnerable position put added weight upon what was taking place. It was a position of weakness for both men, the one placing his hands under the thigh was vulnerable to attack from above. The man whose was above was vulnerable to serious harm by the man who was in a position to cause serious pain and worse. This is just in addition to the notes by Perryman and are conjecture held by some but that makes good sense.