Can a non-immigrant pilot who is licensed to fly work for a USA based regional airline?
Your question is not entirely clear. If you hold a CPL issued by the FAA you still cannot get a job in the USA if you are not a resident or you do not have a “green card” or “work visa” that allows you to be employed here. This is not to say you absolutely cannot get a flying job in the USA but you most likely will have to find a company willing to sponsor you. Given the fact that nearly 10,000 experienced pilots are out of work, including several thousand flight instructors, the odds are not great unless you possess some unique qualification that few other American pilots have, such as the ability to speak Mandarin Chinese fluently, in which case there are a number of contract flight schools that would probably interested in you. I doubt there are any regional airlines that will sponsor you given the glut of qualified pilots looking for employment.