Should i leave my SSN and driver license Number?

Hi everyone,

I have applied an unpaid internship at a non-profit agency. I have already been accepted, but I am required to complete a form with my SSN and Driver license number.
I am not willing to do so because of the concern of Identity theft. Should I complete the form ? Or can I leave a fake number or my ITIN number( Tax Number)? Will there be any problem if I do so?
Thank you very much for your reply.