Shamanism has some roots in the concept of "Sin Eating", but not in the form you've described. In Shamanism the idea of removing "sin" (sickness etc.) from a person, closely resembles the archetype, but with the exception of not taking-on the "sins" of the person, but rather, displacing the sin into another form and sending it away. The Jews had a scapegoat for this function.
Leviticus 16:10 Wrote:New International Version (NIV)
"But the goat chosen by lot as the scapegoat shall be presented alive before the Lord to be used for making atonement by sending it into the wilderness as a scapegoat."