Anyone age 12 or older requesting an original Social Security number card will have to show up for an interview at a Social Security office.

If a parent or a guardian will sign the application on the child’s behalf the child and parent or legal guardian still have to appear.

See Below for the different requirements for:
"How do I get a Social Security Number for my child"

To get a card for yourself:
You will need a Social Security Card Application form.
The first 4 pages are instructions and the last page is the actual application form.

To prove your age (only your age) you need a birth ceritficate.

You will need documents to prove your identity.
Your birth certificate is not acceptable as a primary form of ID.
Documents that you can use include:

U.S. driver's license
State-issued non-driver identification card
U.S. passport
Certificate of Naturalization, Certificate of U.S. Citizenship.
Employee identification card/badge
Medicaid card (issued within the last two years)
Health insurance card (not a Medicare card)
U.S. military identification, U.S. Government identification card
School identity card, certified record, or transcript (current year)
U.S. Indian Tribal card (Social Security has to approve as an acceptable ID)
Certified copy of a medical record
Life insurance policy.

Only originals or certified copies by the issuing agency are acceptable.
No photocopies or notarized copies of documents.

Some documents can be used to prove both citizenship and your identity.

To prove citizenship you would use your U.S. birth certificate or U.S. passport or Certificate of Citizenship or Certificate of Naturalization.

For alien (non-citizens) see the instructions on pages 2 and 3 of the application form.

How do I get a Social Security Number for my child?

It's best to get the number for your child at birth.
Simply apply for a Social Security number for your newborn at the same time that you apply for the birth certificate.

Your baby's information will be shared with Social Security Administration by the state agency that issues birth certificates.

The card will be mailed to you.

If you don't do it then you have to apply at any Social Security office.

But if you wait, you must provide evidence of your child’s age, identity and U.S. citizenship status, as well as proof of your identity.
So it's not worth the aggravation ot procrastinate.

Then Social Security has to verify your child’s birth record with the issuing office.

That can take up to 12 weeks before you get a card.

Are you Adopting?

Social Security can assign a soc. sec. number for your adopted child a number before the adoption is complete.

If you want to claim your child for tax purposes while the adoption is still pending then you have to use the Form W-7A, the Application for Taxpayer Identification Number for Pending U.S. Adoptions.
(download to print it here)

You will have to decide if it might be better for you to to wait, then apply for the number using the child’s new name.

For more information you can download from here here the (Publication No. 05-10023).

This may answer the question, where to get social security card?. Or, Where to get a social security number? Where do I get a social Security number for my child?

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How do I Get a Social Security Number? How Do I Get get a Social Security Card?

How do I Get a Social Security Number?
How Do I Get get a Social Security Card?