Sublime Text, move tabs with keyboard

Nope. However, the following plugin will give you that functionality.

https://github.com/SublimeText/MoveTab

You can install it by pressing Ctrl+Shift+P (Command palette), type/select Package Control: Install Package, then MoveTab.

Then you can immediately move tabs with Ctrl+Shift+PgUp and Ctrl+Shift+PgDn.

On a related note: while this is not the answer to your exact question, many people landing on this page (myself included) may be looking for how to switch tabs with the keyboard.

Here's how to do that:

• Tab navigation:
  • Cycle through open tabs in the order they were opened = Ctrl + Tab / in opposite order they were opened = Ctrl + Shift + Tab
  • Cycle through tabs to the Left / Right = Ctrl + Page Up / Page Down

Source where I learned some of that: https://forum.sublimetext.com/t/switching-tabs-with-keyboard/427