No. A student's tuition credit can only be claimed on one tax return; either the parent's or the student's. In most cases, it's not optional; only the parent can claim it.
Here's a post on the five main points on the 1098-T:
https://ttlc.intuit.com/community/college-education/discussion/re-what-do-i-do-with-form-1098t/01/37...
