Through the power of Django's contrib.admin you can use this tool to figure out (with a decent level of reliability) what version of Django a site is running.
This will only work if contrib.admin is enabled, you can figure out the site's STATIC_URL, and access to the admin CSS isn't otherwise restricted.
djver will detect Django versions from Django 1.4 to Django 1.10.x.
It's probably not a great idea. Just a proof of concept.
pip install git+https://github.com/sesh/djver
Note: right now this is only really tested with Python 3.5
Usage: djver <url> [--static-path=<static-path>] Options: --static-path=<static-path> URL path to the site's static files [default: /static/].
> ./djver.py commoncode.com.au 1.9.10-1.9 > ./djver.py djangoproject.com --static-path=/s/ 1.9.10-1.9