No, that is not correct. Your employer is responsible for fixing it.
When you were on a F visa and have not met the five years exempt period of time, you were not required to pay FICA taxes. See link here: Who is exempt
However, if in the year 2020, your status has changed and you have become a resident for tax purposes, you are required to pay FICA taxes.
If you were required to pay FICA taxes and your employer did not withhold it, I would suggest you communicate with your employer to resolve the issues. They might need to issue you a corrected 2020 W-2 thus you may need to amend your tax return later.
You would need to contact your employer to fix it. If they were not being co-operative, I will suggest you to contact the IRS.
See TurboTax discussion here: FICA withheld
Also see link here: Criminal Act
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