H4 Visa Spouse Tax Filing

You filed 2019 taxes wrong. Since you were married as of December 31, 2019, you cannot file as "Single" filing status. You could only file as Married Filing Jointly or Married Filing Separately (or in rare cases Head of Household if the two of you have been living apart for the latter half of the year and you have a dependent; I will assume that that does not apply).

You must amend your 2019 taxes ASAP to either Married Filing Jointly or Married Filing Separately. Similarly, for 2020 taxes, you must file as either Married Filing Jointly or Married Filing Separately.

For both 2019 and 2020, it is possible for you guys to file as Married Filing Jointly if you both choose to do so. Although your wife does not pass the Substantial Presence Test for either year, and thus would by default be a nonresident alien for both years, since you are a resident alien, you can elect to use the Nonresident Spouse Treated as Resident option (see also the relevant section of Publication 519]). Using this for a given year would make both of you a resident alien for the whole year, and you would have to file as Married Filing Jointly. On the other hand, if you guys do not elect to use this option, you would have to file as Married Filing Separately since nonresident aliens cannot file jointly (without choosing to be treated as resident).

If your wife is treated as resident alien for a given year, her worldwide income for the whole year would be subject to US tax. However, she may use the Foreign Earned Income Exclusion and/or the Foreign Tax Credit to exclude her foreign income from US tax or claim a credit for foreign tax paid, in order to not be taxed twice on the same income. Even if it ends up not resulting in any net US tax on her foreign income, she would still have to report her income on her US tax return (which is you guys's joint US tax return), and file the forms to claim the exclusion and/or credit. The Foreign Earned Income Exclusion can be used during 12-month periods during which she was outside the US for 330 days (she would meet that for 2020 and the parts of 2019 before she came and after she left).

If your wife is not treated as a resident, then she would be a nonresident alien, and she would only be subject to US tax on her US income. I assume that she has no US income, and would thus not need to file a nonresident US tax return (unless you are domiciled in a community property state, in which case half of your income would be considered her income). You would file as Married Filing Separately on your resident tax return, and you would put "NRA" in the space for her SSN/ITIN. She does not need to get an ITIN in this case.

If she needs to get an ITIN, she would file the application for an ITIN (W-7) together with the tax return (or the tax amendment that adds her). She would have to either mail her original passport with the ITIN application (with your tax return), or she would have to go in person to one of the IRS taxpayer assistance centers that offers same-day ITIN passport certification. If it would be too much trouble to apply for an ITIN, another option is to file separately first (which doesn't require her to have an ITIN), and then amend it later to Married Filing Jointly within 3 years when she gets an SSN (or when it is more convenient for her to apply for an ITIN).

If the two of you have different incomes, Married Filing Jointly will almost always result in less tax than Married Filing Separately. You would have to balance that with any additional complications from treating your wife as a resident.