Have you reviewed the chapter on the AOTC in IRS pub 970?
Specifically, read the section on Adjustments to Qualified Education Expenses that begins on page 14.
If when you say that your son is receiving a full scholarship you mean a "full ride" scholarship that covers room and board, he already is getting scholarship money that is taxable income. Whether or not he is required to file a tax return because of this depends on the amount. It's not unusual that scholarship payments are "internal transfers" with no check being issued to the student. Use the billing statements from the school to substantiate where the money comes from and what it is being used for.