You should file as 'Married Filing Separately' OR (if you have another person living with you) 'Head of Household'. You can't file as single because you're not single.
You can file as 'Married Filing Jointly' and include all of your spouse's foreign income and taxes paid on your return. That may entitle you to a bigger deduction. The US government would like me to take this moment to tell you that doing that does not change your spouse's immigration status, just your taxable income.
When you file and list your spouse in TurboTax you will enter "NRA" (for non-resident alien) in the space for their social security number. Once you do this you will not be able to electronically file your tax return, you will have to print and mail it in.
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