Hello

I heard I don't have to pay social security tax and medicare under OPT, but my HR needs documentation to approve it. Could you tell me what the code apply for it and where I can find them? Also, since they already deducted my part and paid their part, can I just let them do that and leave the money there till I get to 65? Is it possible for me to get those money back even though I don't pay them consistently? Thank you so much.

Every one on F1 or OPT is exempt from residency for 5-years. You must file non-resident tax return and you income is not subject to FICA taxes.
Read Publication 519; Tax for Aliens at Internal Revenue Service

Thank you for answering my last questions, but I need to open a new one to ask.
Since I found out early about social security tax and medicare exemption, the payroll office told me that they will return all the taxes including federal, state, and city taxes. But I have to adjust my tax payment at the end of year and pay for the taxes I owed on my own. Because they only can do two ways, either returning all the taxes or paying in full. Is that legal? If they can return all the taxes to me, how can I pay for my taxes at end of year? Thank you.

You will pay the taxes when you file your annual tax returns with the IRS, the state and the city.

Get a statement from your employer as you WHY they are refunding the INCOME taxes, because you WILL be subject to underwithholding penalties from the IRS, the state and the city. If you attach the employer's statement to the return, more than likely, all three tax authorities will waive their under-withholding penalty.

Your employer should only be refunding social security taxes and not income taxes.

Agreed. That is why I told EagleShark to ask for the statement, in hopes that someone in payroll will have a "slap the forehead" moment and realize that they should NOT be refunding the income taxes.