Is there a law that makes it explicitly legal to make traps for non-native species? Or is it just not forbidden?
Well in the US our Constitution lists only those rights reserved to the federal government and all other unspecified rights are reserved to the States and to the People. So you don't generally need a law to say you can do something, but rather a law needs to be passed (federal, State, or local) to state that you can't do something and even then it would have to pass muster from the courts is someone wished to challenge the constitutionality of the law in question. Think of it like arduino I/O pins defaulting to input pins when powered up or reset.
So look out non-protected birds. 
Lefty