"And Abraham said to his servant, the elder of his household" (Genesis 24:2) - for the radiance of his features resembled his own. "Who ruled over all that he had" - for he was master of his own impulse just as Abraham was. "Put now your hand under my thigh" - because circumcision had been given to them through pain, therefore one swears only by it.
Abraham's Trusted Servant and the Oath Sworn by Circumcision
Yalkut Shimoni on Torah 106:5
וַיֹּאמֶר אַבְרָהָם אֶל עַבְדּוֹ זְקַן בֵּיתוֹ, שֶׁהָיָה זִיו אִיקוּנִין שֶׁלּוֹ דּוֹמֶה לוֹ. הַמּוֹשֵׁל בְּכָל אֲשֶׁר לוֹ, שֶׁהוּא שַׁלִּיט בְּיִצְרוֹ כְּמוֹתוֹ. שִׂים נָא יָדְךָ תַּחַת יְרֵכִי, לְפִי שֶׁנִּתְּנָה לָהֶם הַמִּילָה בְּצַעַר לְפִיכָךְ אֵין נִשְׁבָּעִין אֶלָּא בָּהּ.