Can I apply for a social security number while I am on a G4 visa.
Thanks

Depends... if you are with UN, you don't need one, for accuracy, consult HR in your organization.

If you're the staff of an international organisation (UN, IMF, WB,. ), you can apply for an SSN. You need an appointment letter or a similar document.

Spouses and dependents who are also G-4s but do not work for such an international organisation need to get their Employment Authorization Document first. Then, they can apply for an SSN, too.