A social security number is a number issued by the US government to all US citizens and eligible US residents who apply for one.
If your husband earned any income in the US, he will need to file a US tax return. As he has been in the US for 2 years, he is considered a US resident and can use TurboTax to file his taxes.
If he did not earn or receive any income in 2019, he does not need to file US taxes. You can just file married filing separately to declare your taxes.
If he needs to file a US tax return he will need to prepare a Form W-7 requesting an Individual Taxpayer Identification Number (ITIN) and attach the required form and documents to his tax return when mailed. Please see attached form and instructions.
Form W-7 Form W-7 Instructions