It is possible to claim the American Opportunity Credit without an SSN, but you will need a verifiable identification number allowed by the IRS.
According to the IRS
American
Opportunity Tax Credit page,
You may not claim
the AOTC unless you, your spouse (if you are filing a joint return) and the
qualifying student have a valid taxpayer identification number (TIN) issued or
applied for on or before the due date of the
return (including extensions). A TIN is a Social Security number, an
individual taxpayer identification number (ITIN) or an adoption taxpayer
identification number (ATIN).
You may not claim
the AOTC on a later original return or an amended return if the TIN is issued
on or applied for after the due date of the return (including extensions).
