You can’t “file an exemption” for your spouse. A spouse is never a dependent. You either file married filing separately or married filing jointly.
If you file separately, don’t list your spouse or their income on your tax return. Because she does not have a tax number, you will not be able to e-file the separate return, you will have to print and mail it in.
To file jointly, you will have to treat your wife as a US resident for tax purposes. Filing a joint return creates the financial connection to the US that will allow the IRS to issue an ITIN. However, filing jointly means that you will have to include all of your wife’s worldwide income and pay US tax on it. If she also pays tax in a foreign country, you can claim a deduction or credit for that on your US tax return, which should reduce double taxation, but might not completely eliminate it. To file a joint return, you would have to prepare an ITIN application and the joint tax return and mail both of them to the IRS. Once the IRS issues, the ITIN, they will process the tax return.
