פירוש על בראשית 25:33

SWEAR TO ME THIS DAY. When Esau said, “What is this birthright to me? I do not desire it,” Jacob said to him, “Swear to me that you will not desire it, nor will you inherit it forever.” Thereupon he swore to him, and following that he sold it to him, and Jacob gave him the purchase price⁶⁴That is, the money. This is in accordance with the opinion stated above. Although Ramban does not agree with it, he nevertheless mentions it as an alternate interpretation of the verse. or the pottage he desired.
It is possible that Esau said, “What is this birthright to me? It is sold to you,” and Jacob said, “Swear to me that you will never complain about the sale.” And when Scripture says that first he swore to him and then he sold it to him, its intent is as if it said that he sold it to him first and then swore to him.

השבעה לי, seeing that the purchase under discussion was something abstract, the oath would replace the act of physically taking possession of the object purchased and moving it.

ויאמר השעבה לי. He said: "swear it to me on an oath." The reason that Jacob requested an oath from Esau was because the whole institution of the birthright contains many intangibles, such as the honour and dignity conferred on the firstborn. Jacob was particularly interested in the privilege of performing duties in the Temple, something which was the duty of the firstborn at that time. We are conversant with the rule that a person cannot transfer the right to intangibles either by sale or by gift (Maimonides Hilchot Mechirah chapter 22). This is why Jacob insisted on making such acquisition by means of an oath. Yoreh Deah 239 rules that both tangibles and intangibles may be acquired by means of an oath.