My company is undergoing a reorg. Everyone on the team has been accepted into their new team. My job has been posted and the director is interviewing others. I also had a formal interview. The director was told to make a decision by 8/31 and here it is 9/4 and he has informed me that he will not be making a decision until the end of next week. Can I complain to HR? What to do?

You can complain...but are you considering that things may have come up in the business that distracted the director or that you may risk burning a bridge by pushing this up the HR flagpole?

This sounds as though you were terminated, were you? If its posted and you, as well as otehrs must apply this is not a good sign