How to deal with the medical examination with social security card?

No, you can't use social security card for physical examination. But I can tell you how to use the social security card for physical examination.

You can have a look at the physical examination items, and then use the social security card to register in the corresponding window. Then ask the doctor to write you a checklist, and you can use the social security card.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.