how can I check the record of social security card?

The Social Security Office is not in charge of your credit reporting...but your social security number is used to identity you for credit reporting purposes.

To check your credit report for free:
annualcreditreport.com is the real free site to check your credit file for free once a year without a credit card.
https://www.annualcreditreport.com/ - NOT freecreditreport.com -

What kind of record? Lifelong earnings? Who told you to check? You can go to a Social Security Office to get info if it is your card.

You can pay them, but all they can legally tell you is whether that number has ever been issued. They'll be happy to take your money.