Yes, the IRS will accept your tax return if you file married filing jointly with your Non-Resident Alien spouse, even if they don't have a Social Security number. However, you can't e-file and will need to mail your return to the IRS.
You should still apply for a Taxpayer Identification Number (TIN) by filling out Form W-7 and attaching it to your tax return. Here is the link to Form W-7.
If you need to file quickly, you can sometimes take a paper copy of your tax return to a local IRS office to speed up processing. Call ahead to schedule an appointment. Here’s a link to the IRS local office website.
