Can I file without a Social Security Number for my dependent?

You must list the social security number (SSN) or individual tax identification number (ITIN) of any person included on the tax return.

Note: If your dependent does not have and cannot get an SSN, you must list the individual taxpayer identification number (ITIN) or adoption taxpayer identification number (ATIN) instead of an SSN to e-file a return. Otherwise, you will need to paper file the return to include anyone that does not have a social security number or ITIN.

No Social Security Number
If a person for whom you expect to include on your return does not have an SSN, either you or that person should apply for an SSN as soon as possible by filing Form SS-5, Application for a Social Security Card, with the Social Security Administration (SSA). Information about applying for an SSN and Form SS-5 is available at your local SSA office.

It usually takes about 2 weeks to get a SSN. If you do not have a required SSN by the filing due date, you can file Form 4868 for an extension of time to file.

Taxpayer Identification Numbers for Aliens
If your dependent is a resident or nonresident alien who does not have and is not eligible to get an SSN, the IRS will issue your dependent an individual taxpayer identification number (ITIN) instead of an SSN. Write the number in column (2) of line 6c of your Form 1040 or Form 1040A. To apply for an ITIN, use Form W-7, Application for IRS Individual Taxpayer Identification Number.

It usually takes about 30 days to get an ITIN. 

Taxpayer Identification Number for Adoptee's
If you have a child who was placed with you by an authorized placement agency, you may be able to include child on your return. However, if you cannot get an SSN or an ITIN for the child, you must get an adoption taxpayer identification number (ATIN) for the child from the IRS.