Is there a keyboard shortcut to move the position of a tab in Safari?
There does not appear to be a built-in keyboard shortcut to change the position of a given tab amongst other tabs in Safari.  At least none listed in the Apple Support Documents listed below.


Safari 6/7 (Mavericks): Safari shortcuts
Safari 8 (Yosemite): Safari keyboard and other shortcuts
Safari 9 (El Capitan): Safari keyboard and other shortcuts


One might be able to create an Automator Service with a Run Apple Script Action to manipulate tabs in a Safari windows and then assign it a keyboard shortcut in Keyboard System Preferences, however I'd imagine it might not be to easy to code.

Update:

I looked through the Safari AppleScript Dictionary and played around with the coding of an AppleScript script to manipulated tab ordering, or I should say the appearance of tab ordering, as even a simple command such as move last tab to before first tab required a refresh of the URL. In other words whether or not I coded it via move or switching the URL of the current and next tab, etc, all methods I tried forces/requires a refresh of the URL, where dragging and dropping a tab only changes the tab order and does not refresh any tab when done in a DnD manner.

In conclusion, if you don't mind the tab URL being refreshed then the appearance of drag and drop can be accomplished however to physically move a tab without it refreshing would probably require the use of third-party utilities and much more complex coding then coding using move or swapping the URLs of adjacent tabs, etc.