Genesis 24:2 - 3
NKJV - 2 So Abraham said to the oldest servant of his house, who ruled over all that he had, "Please, put your hand under my thigh. 3 And I will make you swear by the LORD, the God of heaven and the God of the earth, that you will not take a wife for my son from the daughters of the Canaanites, among whom I dwell.
For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
This method of swearing hearkens back to the covenant of circumcision. We put our hand on the Bible. I’m not sure if hand under the thigh is a euphemism or just a more socially accepted form of swearing by the covenant.