Brackets? That's easy! Just use parentheses instead!
I guess you mean parentheses. Perhaps I am unaware of some meaning of brackets, that also describes parentheses, but afaik parentheses are different from brackets.
"runde Klammern" for (), "eckige Klammern" for [], and "geschweifte Klammern" for {}.
Although when you say only "Klammern" people usually understand (), because that is what is often used in texts.
This translates well:
runde Klammern --> parentheses, eckige Klammern --> brackets, geschweifte Klammern --> braces.
As such, the US English understanding of the words is clearer to me, than a non-distinguishing understanding.