If "paying off tuition" means paying a debt for past year tuition, the answer is no.
You do get a very generous tax credit for paying current year tuition, 40% of it (up to $1000) is "refundable". That is, you can get it even if you have no calculated tax liability.
But, there's a new urban myth among college students that says they can get a $1000 from the government just for filing a tax form. For most of them, they simply aren't eligible. A full time unmarried student, under age 24, even if you don't qualify as a dependent, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants. You usually must have actually paid tuition, not had it paid by scholarships & grants. It is usually best if the parent claims that credit.
You cannot claim a credit if you are, or can be, claimed as a dependent by someone else.