Are you asking about a dependent or a spouse?
If you are asking about a spouse, are you a US Resident or Non Resident Alien?
If you are a US Resident, then yes, you can file a joint return with your spouse. By doing so, your spouse is choosing to be treated as a US Resident for tax purposes. If your spouse chooses to be treated as an US resident for tax purposes, and you want to file as Married Filing Joint, you can apply for an ITIN when you file your return. You would need to include their income FROM ALL SOURCES WORLDWIDE (not just what they earned in the US) on your return and they would be taxed on it. If you choose filing jointly, you will need to print and mail your return along with the W-7 which is an application for an ITIN and any other required documents to the address in the instructions.
If they do not have an SSN or ITIN and you choose to file Married Filing Separate ,you can enter spouses name and DOB and then on the next screen you can select "xxx is a non resident alien or dual status spouse" Make sure you put a check mark in the box that says My spouse is a Non-Resident alien in the My info section. When you get to the end and try to transmit the return, ignore the e-file errors regarding your NRA spouse and select transmit your return. If that does not work you will need to print and mail your return and write NRA (Non Resident Alien) in the space for their SSN.
If you file as Married Filing Separate, then you would only include your income.
If you are talking about children as dependents, then you may be able to claim them as dependents for the$500 Other Dependent Credit, but you would need to apply for an ITIN for your child when filing your return. You may also be able to claim Head of Household if you are not married or your spouse did not live with you for the last 6 months of the year. You would do this by filling out the W-7 and mailing your return to the address in the instructions.
How should I file my taxes if my spouse is a nonresident alien?
Claiming a Non-Citizen Spouse and Children on Your Taxes
If you are a Non Resident Alien, then you would need to file a 1040 NR which TurboTax does not support, however, our partner Sprintax.com does.