No, not according to the laws at the time. His father was not a citizen and his mother did not meet the requirements of the federal laws at the time, she was only 18 when she had him:
"...The importance to some in arguing that President Obama was born outside of the United States is that, given that t
he President's father was not a U.S. citizen at the time of the President's birth, the federal laws then, in 1961, would have required for citizenship "at birth" of one born outside of the United States to only one citizen-parent, that such citizen- parent have resided in the United States for not less than ten years,
at least five of which were after the age of fourteen (8 U.S.C. ยง1401(a)(7)) (1958 ed.), a requirement that the President's mother, because of her age, would not have met."
https://www.quora.com/Why-don%E2%80%...-to-be-US-born