Abraham called his servant to go into his homeland and find a wife for Isaac. They made the agreement by the servant gripping under Abraham’s thigh.
The demonstration of the oath is likely one used to show submission to the other party’s authority. So the servant was showing his submission to the authority that Abraham bore.
The Obedience
Let’s consider the obedience of the servent here too. He travelled for days back to Abraham’s homeland hoping that a girl might come out and blindly follow him back to his new home.