Yes, but it has to be reported by entering the 1098-T and all other education expenses if the student is your dependent.
If the student is not your dependent, no, only the taxpayer claiming the student's exemption reports the 1098-T, all other education expenses, and applies for an education credit.
The student (if a non-dependent) or the taxpayer claiming the student's exemption claims all education expenses paid by you, or anyone else, made on behalf of the student.
