Swear to me first: for discussion of Swear see 21.23. First translates the Hebrew word “today” as in verse 31. Before Jacob will give Esau the food, Esau must first take a vow, swear to turn over his rights as the firstborn to Jacob.
So he swore to him, and sold his birthright to Jacob: the narrator affirms that the transaction took place. Sold should be rendered as in verse 31.
Quoted with permission from Reyburn, William D. and Fry, Euan McG. A Handbook on Genesis. (UBS Helps for Translators). New York: UBS, 1997. For this and other handbooks for translators see here .