Answer:
No. His father is a Kenyan citizen, and was born in what is now called Kenya, but Barack Obama was born in Hawaii. While Barack spent some time as a child in Indonesia, and (very) briefly in Kenya, the majority of his childhood was in Hawaii. He moved to Illinois to attend college, and has lived there the majority of this life now.
He is a U.S. citizen by both birth - his mother is a U.S. citizen - and by the 14th Amendment, having been born inside the physical geography of the United States.