Unfortunately, you cannot claim him as a dependent. However, you can still file as married filing separately.
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 asked to enter the spouse's Social Security number enter a 'dummy" SSN 999-88-9999. You can only print and mail your tax return, it cannot be e-filed. When you print the tax return "white-out" the Social Security number for your spouse and manually enter NRA for a 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
[Edited 03.18.20 | 3:33 pm]
