Generally, you can't apply for an ITIN except by filing a tax return. (There are a small number of limited exceptions.)
If you are a US taxpayer (citizen or resident alien) married to a non-resident alien you have two choices.
You can file as married filing separately. You do not list your spouse as a dependent. Leave the spouse's SSN blank. You will be prevented from e-filing. Print your return, write "NRA" for the spouse's SSN, and mail in your return. Married filing separately has higher tax rates and some deductions and credits are reduced or disallowed.
Or, you can elect to treat your spouse as a US resident for tax purposes. This means you can file as married filing jointly, which has lower rates and better deductions. But it means you must report and pay US tax on your spouse's worldwide income (subject to a deduction for foreign taxes that they paid). You still can't e-file, and you will have to use a fake SSN to get through the health care section (try 999-88-9999). Then print the tax return, use some white out to blank the fake SSN and write "applied for". Also download and print a form W-7 to apply for an ITIN (international tax ID number) for your spouse. Mail the tax return and the W-7 to the address in the W-7 instructions, not the normal tax return mailing address.
Your spouse will need to sign the W-7 and provide some identity documentation so read the instructions carefully. You will either need to use international courier services to move documents around, or you can file for the automatic extension request and then complete the tax return and W-7 application when your spouse is in the US in May.
You may still need to use a fake ITIN to process the request for extension, and mail in the request instead of e-filing it.
More info here,
https://www.irs.gov/individuals/international-taxpayers/u-s-citizens-and-resident-aliens-abroad-nonr...
https://www.irs.gov/publications/p519/index.html
https://www.irs.gov/uac/about-form-w7
