Bruce R. McConkie describes the oath and covenant of the priesthood.
Bruce R. McConkie, A New Witness for the Articles of Faith (Salt Lake City, UT: Deseret Book, 1985), 312–313
When we receive the Melchizedek Priesthood, we enter into a covenant with the Lord. It is the covenant of exaltation. . . . That there neither is nor can be a covenant more wondrous and great is self-evident. This covenant, made when the priesthood is received, is renewed when the recipient enters the order of eternal marriage.
It takes two parties to make a covenant, but any person alone can swear an oath. Man and Deity enter into the covenant of the priesthood, but only the Lord, meaning the Father, swears the oath.