Translation of Dr. rer. nat. outside of Germany
In the US, most doctorates in science and engineering are also a PhD even though our degrees aren't in philosophy. While other degrees exist, they are less common. I would suggest translating your degree as a PhD since most international audiences will understand that you mean an academic doctorate. 

That being said, I was able to get what Dr. rer. nat. meant, too, so you might decide to put that and not worry about it. Most people have the ability to search the internet when they are confused.