Simple answer: you claim it on your return, since he is your dependent.
Technically, nobody "claims the 1098-T". But, since he is your dependent, you are the only one who can claim a tuition credit based on his education. You use the 1098-T as an entry vehicle.
If the student has taxable scholarship (his scholarship $ exceeds his qualified expenses), he would report the excess scholarship on his return. He, too, would use the 1098-T as an entry tool.
