Does my non-U.S. spouse need an FBAR if they have a U.S. Social Security number?

A non-citizen can be a U.S. resident for FBAR purposes, for example as a green-card holder or under the substantial presence test. Holding an SSN isn't one of the tests. Establish your spouse's citizenship or residency, their foreign accounts and the aggregate value.⁠^{[1]Source 1}⁠^{[3]Source 3}

A non-citizen spouse received an SSN during an earlier period in the United States but now lives abroad. The SSN doesn't decide the current FBAR question. What matters is the spouse's status for the reporting year and their foreign accounts.⁠^{[1]Source 1}

Determine whether your spouse was a U.S. citizen or resident in the reporting year. A tax treaty position that treats them as a non-resident for income tax doesn't change their FBAR residency.⁠^{[3]Source 3}⁠^{[2]Source 2}