If YouTube has enabled your channel for monetization, you can link an Adsense account to your YouTube that belongs to a parent.

If neither of your parents has an Adsense account, they can apply for one. 

However, they need to sign up with their own Google/email account, and they will need their own blog or website (or their own YouTube channel) in their name to apply. You should not apply using a parents name - have your parent sign up directly, because your parent will be responsible for the account, and the earnings will be issued to them, and they will need to understand and agree to the Terms of Service.

Your parent can't apply with anything that belongs to you - they need something in their own name, otherwise if they applied with something of yours (like your YT channel), they'd get rejected, because everything of yours is in the name of a minor.