Ha'amek Davar: Presumably, he swore with HaSh-m's name, like Avraham requested. The Torah mentions that he put his hand under his thigh to teach that this is essential for a [Torah] Shevu'ah, like the Rif learns from here (Shevu'os 38b). If not for the repetition, it would seem that it was making a Bris with him (refer to 24:2:1:3).