You can file a “Married Filing Separate” return in your situation, but you must mail it in, and write “NRA” in the spouse’s Social Security number field. As discussed in this other Community thread, you do that by either leaving the field blank (TurboTax should let you continue— there’s an error which lingers on, but it doesn’t matter since you’re not e-filing), or entering a fake number which you subsequently white-out before making your NRA entry.
However, you also have the option of treating her as a U.S. resident (as the IRS tells us here) and filing a joint return. The IRS’s “Interactive Tax Assistant” is a little confusing, but if you’re making the election, then she has a filing requirement. And in that case, you’d select “Filing your own federal tax return” as the reason she’s applying (as it’s her joint return too), and ITA should then give you the “You are eligible...” result on the next screen.
Which is correct, as the IRS clearly states (in many places, including here) that a non-resident alien electing to file a joint return with a spouse who is a U.S. citizen can get an ITIN. You would be taxed on her worldwide income for the entire year on that return though, so you may want to compare the results before deciding on this.
Regarding the exemption question, they’re no longer claimed on federal returns (since 2018) — that’s why the ITA gives you the “ineligible” result if you enter “Being claimed as a spouse on a joint return” as the reason for applying.
@nacnudv8, I hope this is all clear, but don’t hesitate to re-post for additional clarification!
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