Can an employer fire you for getting arrested even if it was outside of the work place and there was not a guilty conviction?

unless you work for a local,state or federal agency they must show some kind of nexus between job and offense.

Yes, if it could cause an image problem for the company, then they have grounds to fire you. Heck, they can fire you if they don't like your personality, you can get fired for just about anything. This might have been a reason to get rid of you.