Is my credit score tied to my Social Security number or to me as a person?

It's tied to your identity file at the credit bureaus, which is keyed largely by your SSN along with your name, birth date, and addresses. That's why your foreign history doesn't follow you and why your U.S. file starts fresh. If you built any history under an ITIN before getting an SSN, ask the bureaus to link those records so your history carries forward once you notify them and the IRS of the new number. Guard your SSN carefully, since it's the key to your credit identity and a target for fraud. Consider a free credit freeze until you actively need credit. The CFPB explains credit files and freezes at consumerfinance.gov.