This is just conjecture, but it looks a lot like Abe Lincoln's. But then it couldn't be his, because he was dead then. That'd mean it has to be one of his relatives who wasn't dead then. That'd at least narrow it down.
Your coin shows little circulation wear, which makes it a nice find for its age. Coins of this year & MM where horded and some have been returned to circulation in recent years due to the passing on of those collections. 1968 was the last year for the high relief dies to be used on cents, with a new master die made and used on the 1969 cent coins.
It wasn't long ago thaty you could find one for 10c. Problem is that yours has a nice looking cameo to it