Most nonresident students and scholars cannot claim family members as dependents. Any family member who can be claimed as a dependent must have a Taxpayer Identification Number (TIN). If the dependent has been issued a Social Security Number (SSN), it is used as the TIN. Most family members do not have work authorization, so they will not have SSNs.
The IRS issues Individual Taxpayer Identification Numbers (ITINs) to individuals who are required to have TINs but who are not eligible to obtain SSNs. The ITIN was created for use on tax returns only.