No, you won't pay tax on this. You won't report it on your tax returns or other documents, either, unless your parents are nonresident aliens.
If that's the case, then you report the information on Form 3520. There is no tax due for filing Form 3520- it is for information only.
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"