If you want to use the ReadTheDocs theme locally with Sphinx you can clone/fork the code from the Github repository below.
Source: https://github.com/snide/sphinx_rtd_theme
If you're also building your Docs using readthedocs.org you'll need to enter the following to your conf.py to avoid issues with the RTD build process:
# on_rtd is whether we are on readthedocs.org, this line of code
grabbed from docs.readthedocs.org
on_rtd = os.environ.get('READTHEDOCS', None) == 'True'
if not on_rtd: # only import and set the theme if we're building docs locally
import sphinx_rtd_theme
html_theme = 'sphinx_rtd_theme'
html_theme_path = [sphinx_rtd_theme.get_html_theme_path()]
Otherwise, readthedocs.org uses their theme by default, so no need to specify it.