In order to file a joint return with him, you must have his agreement, so you can ask him for his SSN if you do not know it. Or....look for it on a past tax return that the two of you have filed together. If he does not agree to file a joint return, then you can file married filing separately, or if you have children, perhaps file Head of Household. You do not need his SSN to file HOH.
If you have filed past returns with TurboTax
To get a copy of your previously filed returns prepared with online TurboTax https://ttlc.intuit.com/questions/1900748-how-do-i-get-a-copy-of-a-return-i-filed-in-turbotax-online