Social Security Number
To work in the United States you must have a Social Security Number. You may start working without a Social Security Number as long as you provide evidence to your employer that you have applied for one. If you have a Social Security Number you should use it when completing your tax forms.
If you are an F-1 visa holder with on-campus employment, you must first obtain a job offer letter from your on-campus employer.
A Social Security Number card is an important document and should be kept in a safe place to avoid identity theft.
If You Are Not Eligible for a Social Security Number
The US government restricts the issuance of new Social Security Numbers (SSN) to individuals who are employed. However, SSNs have come to be used for many other purposes such as opening a bank account, buying a cell phone and/or obtaining a credit card.
You will be able to open a bank account without a Social Security Number. However, in this case, you will need to show two forms of identification. If you do not have your ID yet, the Form I-20 should be acceptable along with your passport. You will also need to provide a local address.