Yes. You can claim the education credit for you and your son if he is your dependent. If he is under 24 years old and a full-time student, his income is not an issue in dependency as long as he didn't pay over 1/2 of his own support.

Whoever claims your son (you or himself) will claim the credit regardless of who pays the tuition.

Also, remember that your son should say he's a dependent on another return when he files his own return. His $6,000 doesn't go on your return. 

If you have any other details regarding this question, please feel free to post them in the comment section.