"나는 미국에서 왔어."
Translation:I am from America.
I'm not sure if a native will understand it the way you are meaning it (I'm not native), but as a literal translation, it seems correct too, indeed.
However, note that this structure seems to be used most often as an answer to this question:
어디에서 왔어요? Where are you from? (like in, which country are you from?)
That makes it sound like you're on a trip around the world, you've recently arrived in whatever country you're now in, and before that you were in America, whether that's your home or not.
For instance: I'm from Australia and I'm currently in Korea. I came from Japan. The ferry to Busan was very relaxing.
AMERICA is a continent. United states of America is a country so everyone who was born in a country of the american continent is american. Every American is american but not all american are American. Therefore translating 미국에서 as America is completely wrong In fact... America in korean is "amerika"