Can I apply for an ID card with a social security card?

You can't. The social security card is not a valid identity document, so it is not necessary to reissue the identity card. When you go to apply for a permit, you should bring your household registration book and two color photos of yourself. When going through the formalities, you should fill in the registration form of resident ID card application, collect the fingerprint of ID card, and help the staff to accurately check the registration items of ID card and pay the registration fee.