I'm not aware of any faculty unions representing professors. There are some academic student employee (inc. grad students) unions and a handful of postdoc unions.
Additionally there are not-officially recognized groups such as AAUP (American Association of University Professionals) that represent faculty issues.
faculty actually refers to the body of faculty at a university or in a department as a whole...when writing to certain communities
What I meant was that certain universities have the whole body of faculty unionized