If you are a US citizen and your spouse does not have a Social Security number or an ITIN and you are not applying for an ITIN with the tax return then you can only file your tax return as Married Filing Separately.  

Where you are asked to enter the spouse's Social Security number enter 999-88-9999.  You can only print and mail your tax return; it cannot be e-filed.  When you print the tax return erase the Social Security number for your spouse and manually enter NRA for non-resident alien.

See this TurboTax support FAQ for the procedure to print and mail a tax return using the online editions - https://ttlc.intuit.com/questions/1944348-how-do-i-print-and-mail-my-return-in-turbotax-online

If you are filing your tax return as Married Filing Jointly you must apply for an ITIN with the tax return and you would need to be providing a statement with your tax return that you want your Nonresident Alien Spouse Treated as a Resident.  See IRS Publication 54 Tax Guide for U.S. Citizens and Resident Aliens Abroad pages 6 and 7 - https://www.irs.gov/pub/irs-pdf/p54.pdf

Go to this IRS website for ITIN information - https://www.irs.gov/individuals/international-taxpayers/general-itin-information

How do I file with a W-7?

TurboTax doesn't include Form W-7, so you'll have to download it directly from the IRS, fill it in, and print it out (see these IRS instructions for help with that).

Then, complete your return as you normally would. Leave the applicant's Social Security Number field blank, and disregard any warnings about the empty field or missing health care info for the applicant.

When your return is finished, go to the File section and follow the steps to print a paper copy of your return, as you won't be able to e-file with a missing SSN.

Bring your printed, signed return (along with any attachments per the filing instructions, such as W-2s or 1099s), the completed W-7, proof of identity, and foreign status documents to your acceptance agent or an IRS Taxpayer Assistance Center.

Alternatively, you can mail everything to:

Internal Revenue Service
Austin Service Center
ITIN Operation
P.O. Box 149342
Austin, TX 78714-9342

See also General ITIN Information at IRS.gov.

Each person on the tax return needs either a SSN or ITIN number in order to successfully e-file.  The Individual Tax Identification Number, or ITIN, allows taxpayers who don't have a Social Security Number (SSN) to file income tax returns. Unlike other forms of ID, ITINs only have one purpose—tax filing and reporting.

Both resident and nonresident aliens may obtain ITINs regardless of immigration status. Nonresident and resident aliens, their spouses and dependents can apply for an ITIN if they are not eligible for an SSN. Here’s who might need an ITIN:

• Nonresident aliens who are required to file a tax return
• Resident aliens who are required to file a tax return due to the number of days they reside in the U.S.
• Dependents or the spouse of a U.S. citizen or resident alien
• Dependents or spouse of nonresident alien visa holders

Tax filers who live abroad can also obtain an ITIN.   Nonresident Alien Spouse - IRS options

How do I get an Individual Taxpayer Identification Number (ITIN)?