In iOS 7 Safari, at first, it's perhaps counter-intuitive how to move a folder of bookmarks. However, once you get the hang of it, it's easy. Here's how to do it.
The best way to show this is with a real world example. I have a Safari bookmark folder labeled "TMO-editor". For the sake of this example, let's say I want to move that folder into a folder labeled "Archive." Here are the steps.
1. On the bottom right of the bookmark list, tap "Edit." The list will look like this:
2. Tap the name of the folder to be moved. In this case "TMO-Editor." Be careful not to tap the red delete prompt on the left or the re-order icon on the right.
You'll see "Edit Folder" at the top. (See screen shot above.) This is prompting you to select a new location for the folder "TMO-editor" and showing that it's currently in "Bookmarks." Tap the name of the current location. In this case "Bookmarks >."
3. Tap the new destination name. In this case, tap "Archive." Then, you'll see that the new Location is "Archive >."
4. Return to Bookmarks by tapping at the top left. The folder "TMO-editor" has been moved to the Archive folder. You're done.
If you open, in this case, the Archive folder, you'll see that the "TMO-editor" folder has been added at the bottom. If you want to reposition it, tap "Edit" and use the re-order icon to slide it upwards. Again, when finished, tap "Done."
I found that once you get the hang of moving folders around, it's not as confusing as it may have seemed at first.
Teaser bookmark via Shutterstock.