Who was the first AFC team to win the Super Bowl?

Either the Green Bay Packers or the Kansas City Chiefs, depending on exactly what you mean by "first Super Bowl".

The first "world championship game"... that we today in hindsight would call Super Bowl I ... was won by the Packers, who beat the Chiefs for the title.

The first championship game that was actually officially called the "Super Bowl" was played 3 years later, and that one was won by the Chiefs (particularly fitting, since the team's owner was one of the people who had suggested the name "Super Bowl" in the first place) who beat the Vikings.