If you are offered a job in the U.S. (including on-campus), you will need a Social Security Number. To obtain a SSN, you will need to submit the On Campus Employment Verification. Bring that form to an International Office (IO) advisor, who will give you an authorization letter and instructions on how to apply for the Social Security Number.
Proof of employment is a requirement to apply for a SSN. If you do not have a job offer, you are not eligible for a SSN.
For more information about requirements for a SSN
In general, F-1/J-1 students who have been in the U.S. less than five (5) years are exempt from Social Security (also known as FICA) and Medicare taxes. Be sure to bring this to the attention of your employer as many are unfamiliar with this provision of the tax laws. Students in F-1/J-1 status are subject to all other federal, state, and local taxes that apply. For more information , please visit the IRS Webpage: Alien Liability for Social Security and Medicare Taxes of Foreign Teachers, Foreign Researchers, and Other Foreign Professionals