Great-grandfather was born in the US, am I eligible for citizenship?

I am aware that this is very far fetched, however I just want to know if there is any possibility. My great-grandfather's family moved to the US, I even have the Ellis Island registry page, and he was born there and lived there as an US citizen. During adulthood he moved to Romania, Europe and started a family there. The Communist regime stole his birth certificate and neither his children or their children have tried to apply for citizenship. Now I am here, first is it possible for me to apply in any way for citizenship, also is it at least possible to find his birth certificate in any registry, it would really put my grandmother at ease.

Thank you very much!