Since Unity became the default DE in Ubuntu, it’s not easy to customize the panel. Appication indicators used to be movable by right-clicking on icons, but now unity’s panel indicator doesn’t.
For now there’s not any tweak tool but only editing the configuration file can change the indicators’ order.
For global, all user will take effect by editing
/usr/share/indicator-application/ordering-override.keyfile. Here use gedit:
sudo gedit /usr/share/indicator-application/ordering-override.keyfile
In picture the value of indicators 1 ~ 5 means the icons order in top-panel from right to left. You can change the order by changing the value, or add new item (you need to know the indicator’s name).
If you only want this working with current user, create and edit this file:
copy and paste previous order (see the picture) and then change it as your like.