How to enable auto-complete in Emacs Org-babel?

You can switch to a dedicated session with the right mode and auto-completion simply with C-c C-v z when you are in a code block.

C-c C-v z or C-c C-v org-babel-switch-to-session-with-code

Check the org-documentation 14.11 Key bindings and useful functions for more information.

Late to the party but today the default (and recommended way without other hacks) is to switch to the dedicated elisp buffer for that "hunk" using 'org-edit-special which today is mapped to

C-c- '

Hit the same to return to your org file editing.