If a white South African moved to the USA, would they become African-American? South Africa is the African country with the most white people, although not the only one. My question really would apply to any white African moving to the USA though. Would it be correct to call them “African-American”?
While they were in Africa they were euro Africans, If they came to the U.s. they would be Euro Americans.
No.
If I put a beagle in the oven would that make him a hotdog? Why do we park in the driveway and drive on the parkway? Why do we call them buildings when we’re already done building them, should we call them built? Why is “Let’s eat, Grandma” a different sentence than “Let’s eat Grandma”? Why does inflammable mean flammable? Why does “the house burned down” and “the house burned up” mean the same thing?
It turns out that natural languages are not generated or parsed according to universal logical rules. We have homonyms, words have different meanings in different contexts.
And so “African-American” is not a word that means people who were born in Africa who now live in America. It would be logical if it did, but it doesn’t, so it isn’t.
Sometimes it is used as a Ctrl+F of “black,” but more appropriately it refers to people who have a shared experience of being descended from slaves in the USA. Whether this category includes say, Colin Powell (Jamaican parents) is a debate for another time.
You also generally don’t become any type of hyphenated-American until you get citizenship; mere moving isn’t enough.
There are many African countries with many, many more “white” people than South Africa, although I suspect you mean Sub-Saharan Africa.
I can’t believe the OP was sincere.
Maybe he had Charlize Theron in mind when he wrote the OP. 
(Born in South Africa, became a U.S. citizen in 2007.)
Whenever I see my wife’s cousin’s kids I get a kick out of “African-American” as a title.
Her white South American cousin moved to South Africa and married a white guy over there. Thus, her blond-haired fair-skinned offspring are as African and American as one can get, following the letter of the expression, if not the true spirit.
Then there’s the whole question of Colin Powell.
In the scenario in the OP, I think South African American would be most accurate.
Most people who immigrate to the US just become “Americans.” I know a very darkly complexioned fellow from Nigeria who immigrated and he gets really offended if anyone refers to him as an “African-American.”
No more than an Israeli moving to the US would become an Asian-American.
My family is Irish/German-American.
My brother married a white South African woman, and they have two sons.
My sister married a black guy from Guyana (South America). They have a daughter and a son.
I like to joke that my brother’s kids are white African-Americans, and my sister’s are black Irish-Americans.
Of course, I don’t actually regard my brother’s kids as African-Americans. However, in the restricted sense, neither are my sister’s kids.
Or maybe Black Irish-Americans?
All of this makes the decision about which bathroom to use seem relatively straightforward.
I know a black man who, while an American citizen, was actually born in Sweden. He loves to introduce himself as a Swedish-American.
Sure. His nationality is Nigerian, or American if naturalized. His ethnicity is Yoruba, or Hausa, or whatever.
As a white South African living in the US I’ve heard this a number of times. As others have said, its silly. African-American is used to describe black Americans. If I had to call myself anything it would be South African-American, analogous to Irish-American, etc., although in practice I never do. In fact, it seems weird to me to call a black person who moved from an African country to the US African-American. It seems more natural to call them Nigerian-American or Somali-American or whatever specific country they came from. But its not like its an exact science. As far as I know its still common to refer to people as belonging to say the Irish-American community even though they’re from a family that has been born in the US for a number of generations.
So in short, its complicated and difficult to explain, yet I think everyone knows what African-American means, and if you use it to describe a white South African you’re deliberately being obtuse.
A bit of little known trivia: Barack Obama is descended from a slave in the USA. But not on his Nigerian father’s side. His white mother had a slave ancestor.
I knew a white South African lady who lived her for quite a while. The Thais refused to believe she was from Africa, because she was not black.