As a J-1 resident alien, can I file as married filing jointly?

Yes, absolutely.  Since you are a US resident, you can file an election to claim your non-resident spouse as a resident and file jointly.  TurboTax does not provide any tools or forms to assist you to make the election, unfortunately.  You would need to follow IRS's instructions to attach the statement to your 2020 tax return.  You cannot e-file.  Instead, print out all your tax forms along with the statement and paper-file.  Click here to see Nonresident to resident

Hi, I am in an exactly similar situation when filing for 2021 returns ( I am on J1 Visa but a resident for 2021, and my wife, J2 arrived in 2021 is non-resident). I am inclined to file jointly, but can you give me a little more detail on what details should go into the declaration, and if any additional documents need to be attached with it? 

Yes, here is a summary what needs to be done and the documentation required.

1. Prepare your return in TurboTax.
2. When you get to the Let’s get ready to e-file screen, select File by Mail.
3. Attach a statement to your return, signed by each of you that states that one of you is a U.S. citizen and the other is a nonresident alien and that you’re electing to both be treated as U.S. residents for tax purposes. Include the full name, address and Social Security number (or Individual Taxpayer Identification Number) of each spouse. This won’t affect the immigration status of the nonresident alien.
4. Mail the return to the address on the instruction sheet that prints with the return.

If your spouse doesn’t have a Social Security number or ITIN, you’ll need to apply for one when you mail in your return. To do this, follow steps 1–3 above and then do this:

1. Fill out Form W-7 and attach it to your return, as well as all necessary documentation.
2. Mail the return to the address specified in the Form W-7 instructions.

Note: TurboTax will give you an error regarding the missing Social Security number for your spouse. You can ignore the error since you’re printing your return.

@sabyasachi2321

Hi, I am in a similar but slightly different situation. I am on a J-1 visa and have filed taxes as a non-resident alien in 2022 and 2023, and I have to file taxes as a resident alien in 2024. My wife and two children arrived at the same time as myself, and they are resident aliens but do not have SSN or ITIN. 

What are the advantages of applying for an ITIN, and would it be possible to go without applying for it? We are leaving the US this year, so I do not want to apply if it is too much of a hassle.

If your spouse is a non-resident and had no earned income, you can file as Married Filing Separately and leave your spouse and children off your return.  However, you will need to mail your return, as your spouse doesn't have a SSN or ITIN.

Here's more info on Filing with Non Resident Spouse and Tax Tips for Resident and Non-Resident Aliens.

@Sato2 

Thanks! My wife is on a J-2 visa and has been in the US since April 2022, so if my understanding is correct, I believe she is a resident alien. If I decide to file separately, does she also have to file something? She has no income in the US or any other country.

If your spouse qualifies as a resident alien with the substantial presence test, you'll get a better refund if you add her and your children to your return.  You'll still need to mail your return, for lack of SSN/ITIN's.

You could mail your return with a Form W-7 attached to apply for an ITIN, but if you're leaving the country, you may not want to.  It takes longer to process a return with a W-7 attached.

@Sato2 

Thank you so much! This is very helpful. 

If we decide not to apply for ITIN, then does my wife (who is a resident alien with no income) have to file tax anyway or is that not necessary?

I'm probably asking a very naive question... If no income, is filing not mandatory?

No, filing is not mandatory, if your income is below the Standard Deduction for your Filing Status.

However, many choose to file to get any tax withheld refunded. 

@Sato2