Polish Work Visa For US Citizen

A company needs to arrange this and to do so they need to prove that there is no one else suitable for hiring.

You can't get a work permit on your own.

Ruth

As posted by *1 - everbrite, either the company or an affiliated agent for the company are the only means.
If you have a highly skilled profession (doctor, professor etc.), there's a chance you can be 'Fast-tracked'.
However, it still requires all the correct paperwork to be processed.
Good luck with everything.

US citizens working in science (at universities, research institutes) are exempt from getting a work permit.

They'd still need the proper paperwork though, regardless.