When each of the swear participants agree to penetrate the other's anal cavity with their own pinky and then swear upon the decided promise.
Joe and Nathan both agree to each other that they do not want anyone else to know about them cheating on their math exams. To make a seal of silence they agree to engage in a "Stinky Swear". Joe inserts his pinky into Nathan's anal cavity, while Nathan inserts his pinky into Joe's. While the penetration is occuring, they both verbally agree that they will not tell anyone about their cheating on the math exams.