A: Yes, you can.
Parolees from several countries who have been granted humanitarian parole may be eligible to apply for a U.S. social security number. There are two potential methods.
(1) You can either apply directly to the Social Security Administration, or (2) you may apply for one when you file Form I-765 Application for an Employment Authorization Document (EAD).
A humanitarian parolee with only a Form I-94 or a parole stamp in their passport may only apply for a non-work Social Security number (SSN). If you are applying for benefits, your local welfare or social service agency should provide you with a referral letter to the Social Security Administration explaining that the agency needs your SSN in order to process your application for benefits. With this letter, the Social Security Administration will accept your application for an SSN.
To apply for a non-work SSN directly through the Social Security Administration, fill out the application for a Social Security Card and print the application. Bring it to your nearest Social Security Administration office, along with your passport, I-94, birth certificate, marriage certificate, and the referral letter from the welfare or social services agency. You may need to make an appointment in advance at the Social Security Administration. Prepare translations of any required documents in advance.
The link for the social security card application can be found at https://www.ssa.gov/forms/ss-5.pdf
You can look up the closest Social Security Administration office at https://secure.ssa.gov/ICON/main.jsp#officeResults
You may also apply for a social security number when you apply for your work permit, which can be provided to employers. When filling out your Form I-765 – Application for Employment Authorization Document (EAD), check boxes 14 and 15 to receive a Social Security Card. You may do this even if you previously received a non-work SSN. The information you provide on this form will then be sent to the Social Security Administration to issue you a social security card.
Once you receive your Social Security Card, please remember to sign it, and keep it in a safe place (it is not advisable to carry it on your person).
Here is a guidance from the SSA office: https://secure.ssa.gov/poms.nsf/lnx/0110211600
Here is an application for a work permit, which can be filed online at USCIS website: https://www.uscis.gov/i-765