Java has dynamic arrays called ArrayList.
But your solution doesn't need them, just think about what Chrono79 said.
It is possible to know its size beforehand.

Strings in Java are immutable, but if you reassign them, your command should do what you want.
str = str.replaceAll(" ","");
If you want to remove all non-visible characters (e.g. tab, \n), go with:
str = str.replaceAll("\s+","")