You will need to contact the Social Security Administration, as the IRS does not issue SSNs.  Use Form SS-5-FS (PDF), Application For A Social Security Card, which may be obtained from and filed with the Social Security Administration.

For foreign born children, review the article found on the SSA’s website entitled "Obtaining a Social Security number for a foreign born child."

If you are a U.S. citizen or permanent resident and you are now married to a nonresident alien, you should contact the U.S. Citizenship and Immigration Services (USCIS) to assist you in determining if your spouse is eligible to obtain a Social Security Number (SSN).

Each foreign person who does not have and cannot obtain a SSN, must use an IRS Individual Taxpayer Identification Number (ITIN) on any U.S. tax return or refund claim filed. For additional information on ITINs, refer to FAQs on Individual Taxpayer Identification Number and the Instructions for Form W-7 (PDF), Application for IRS Individual Taxpayer Identification Number.