In the picture the child is having fun with her tongue. Is it called a tongue twister?
No, a "tongue twister" is a sentence that is very difficult to say correctly.
- She sells seashells on the seashore
- The sixth sheik's sixth sheep's sick.
- Which wristwatches are Swiss wristwatches?
What the child in the picture is doing is called tongue rolling. See Tongue rolling on Wikipedia for more information.
I can't speak for England, but in America I have always heard people say "She can roll her tongue." Just as a point of clarification, because based on the above, you might think it's appropriate to say "She can do tongue rolling." If you said that to me, I would have no idea what you were talking about, but I might fear it was something sexual.