Jzaldana1,
The answer is that it depends. Chances are you will either file as Married Filing Joint or Married Filing Separately. However, if your wife is (or was, at any part of the year), a non-resident (or "dual-status") alien, you could file as head of household separate from your spouse if you have a qualifying dependent (such as a son or daughter) for whom you provide at least 1/2 of the household support. The most advantageous status to use for your return could depend on whether your wife can be considered as a resident or not. She can be considered to be a resident automatically if she was physically present in the United States for at least 183 days in 2019 and not under certain types of visas (such as student, teacher or professional visas, for example). Even if this is not the case, you (as a couple) can elect for her to be considered a resident for tax purposes by attaching a statement to the 2019 tax return stating that you wish to make this election. You would make this election to use the status "Married Filing Jointly", which is likely your most advantageous filing status.
However, there will be another step. Since she does not have a Social Security Number, you may need to apply for an ITIN (Individual Tax Identification Number). For more information on how to apply, please see the following link: IRS ITIN website. You will notice that the website makes reference to Form W-7. This Form is not available in TurboTax but can be downloaded from the website link above. (It is a fillable PDF that you can attach to the tax return).
I hope this information is helpful, but feel free to reach out if you have additional questions.
Daniel
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