Is the SMS notification fee for social security card free?

There is no SMS notification on social security card. I think you're asking about SMS notification of social security deduction. There are two kinds of SMS notifications. One is a warm reminder from the Social Security Bureau to remind you to deduct money. This one is free of charge, and the other one is the SMS notification caused by the change of your bank account due to the deduction. This is a banking business, and there is usually a charge.