If you are eligible for an SSN, apply now. If you are in F-1 status and have an on-campus job or are a PhD student, you are all eligible to apply for an SSN. If you are a J-1 student you are eligible to apply for an SSN.
Students receiving taxable scholarships will use an ITIN for tax reporting purposes if they are not eligible for a SSN.
Please review the quick guidance listed here. Upon receiving your SSN or ITIN, bring your card to your registrar so your Yale record can be updated.
If you are receiving scholarship, stipend or are working on campus you will need to file a 2018 tax return and will need to an SSN or ITIN. If you take care of that now and report to your Registrar before the end of this semester, filing your 2018 tax return will be much easier.