No. Although some schools still use the SSN as a student identifier, the Social Security Administration strongly discourages this practice. Schools are not authorized to use SSNs to administer educational programs and Social Security cannot assign an SSN for this purpose. The Security only can issue an SSN to:

• U.S. citizens;
• Noncitizens deemed eligible to work by the Department of Homeland Security;
• Noncitizens who already have qualified for a government benefit or service and are required by law to provide a Social Security number.

If your college asks you to provide an SSN and you do not have one or you prefer not to provide it, ask the school to assign an internal number for administrative purposes.