I keep hearing about her being half black but I have yet to see any proof. Alex and her mom have hair way too straight to be of significant african descent. But this isn't exactly a very realistic show so hair might not equal heritage. So I did some digging. One of the episodes commonly cited for her heritage is "Alex Get's Schooled" https://www.youtube.com/watch?v=fDi7MmoxzJ4
Her parents show up in this one, which is what people use to guess her race. Her dad is white (in this appearance) and her mom is just as ambiguously brown as she is. Race and ancestry are never mentioned. The episode where she researches her family tree is "Evil Gymnasts" https://www.youtube.com/watch?v=BSK5YL5DSvc
In this one Alex's mom sends her the family tree, which is never pictured or described. Alex believes she has some cousins in France. Which by the end of the episode we find out is false and the people she believes to be her cousins turn out to be complete strangers.
I don't think that we ever even get a last name for her at any point in the whole series. With that straight hair I always assumed she was some variety of jungle asian. Y'know Filipino, Thai, Vietnamese. But I'd buy her being Mexican or South American as well.