You should leave it blank.
You might need to apply for an ITIN for her. Per IRS, if your spouse is a nonresident alien, he or she must have either an SSN or ITIN if :
1. You file a joint return or
2. You file a separate return and claim an exemption for your spouse, or
3. Your spouse is filing a separate return.
For filing status, you can file either Married Filing Jointly ( see Nonresident to resident ) or simply Married Filing Separate.
[ In the TurboTax program, you would follow the step-by-step interview questions to choose the appropriate filing status, enter your spouse information and leave the SSN blank, after print out the return , you can leave it blank or hand-write APPLIED in the space.]
If you want to file Married Filing Separate, you can qualify for an exemption for your spouse only if:
- Your spouse had no gross income.
-- Your spouse won't file a tax return.
- Your spouse didn't qualify as the dependent of another taxpayer.
Additionally, you cannot e-file a tax return which does not include a SSN or ITIN. If you fall under one of the above conditions, you will have to manually apply for an Individual Taxpayer Identification Number ITIN on Form W-7 for her.
See https://www.irs.gov/Individuals/General-ITIN-Information.
Although you cannot e-file, you can still use the TurboTax program to prepare your tax return and required forms. Then print, attach to the Form W-7 with the required documentation ( see the above link ) and submit everything to the IRS Austin location in Texas by mail.