I thought the circles were listed in alphabetical order, and started prefixing them like "1-Family", "3-Acquaintances", "9-Strangers" but now I added a "5" which is listed last in the circles screen and in dropdown lists.
What's the sorting logic, and can it be influenced?
(Of course this could be a feature they're still working on.)
Just announced: You can now manually re-order your Circles.
Announcement on Google+ by a Google Engineer, with video
It's now basically as easy as:
Left to right will appear highest to lowest on the sidebar when viewing your stream and wherever else your circles list appears.
The short answer is you can't.
There are some articles that claim if you rename the circles and prefix the names with 1,2,3, etc that will reorder them. I have tried this and it doesn't work (and judging by most of the comments it doesn't work for anyone else either).
I would imagine it is still in development or they haven't thought of implementing it. Either way I would suggest that you submit feedback just to make sure.
Ordering circles in G+ in a browser doesn't work, but prefixing them with numbers will change their order in the mobile app. It'll look like garbage in a web browser then because you'll have a bunch of out-of-order numbers, but if your main access to G+ is via the mobile app then it may be enough.
You can re-order (sort of) if you are willing to do it manually.
You'll notice that the circles are positioned in the order that you created them. If you want them re-ordered, you need to delete them and recreate them in the order you want them. It's a pain in the butt but it works. Happily when you create a replicate circle, you can drag the members from the first into the new group and then delete the original circle.
It took me about five minutes to do this with 10 circles.
I also had the same problem. Then I discovered randomly, that after I have switched to the new Google Plus, and soon after having reversed to the old Plus... whoo-hoo! The circles just appeared again, in such a way arranged that could be rearranged - and was as simply as to hold one of them and drag and drop to the desired position.
