Yes, there is a way to pay the TurboTax (TT) fee with your federal refund. That will be an option at the end of the TT program.
But, you don't "file a 1098-T form". You file a regular tax return (form 1040 plus any attachment forms), which may include claiming a tuition credit. The 1098-T is only an informational document. The numbers on it are not required to be entered onto your tax return. However receipt of a 1098-T frequently means you are either eligible for a tuition credit or possibly the student has taxable scholarship income.
If you claim the tuition credit, you do need to report that you got one or that you qualify for an exception (the TurboTax interview will handle this)
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. 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.
Reference: Line 7 instructions for form 8863. https://www.irs.gov/instructions/i8863
