There is a wide range of themes to change the default look of how the .. code:: directive handles. For instance:
.. code:: $ curl -i "https://api.github.com/repos/vmg/redcarpet/issues?state=closed"
Outputs with the default theme:

With the sphinx_bootstrap_theme:

However, if you wanted to create a closer feel to the github documents you can extend the default css and use the .. raw:: directive to call a custom class. I created a _static/cli.css file in my docs directory with the following:
.cli { border: 1px solid #cacaca; font: 12px/1.4em Consolas, 'Liberation Mono', Courier, monospace; padding: 10px; overflow:auto; border-radius: 3px; margin: 2em 0; background-color: #444; color: #fff; position: relative; }
Then added the following to the conf.py. There are other ways to extend the CSS, but this is just the one I choose at the time.
html_static_path = ['_static'] def setup(app): app.add_stylesheet('cli.css')
Finally in the rst I called the new class using the .. raw:: directive.
.. raw:: html <div class='cli'> $ curl -i "https://api.github.com/repos/vmg/redcarpet/issues?state=closed" <br> $ curl -i "https://api.github.com/repos/vmg/redcarpet/issues?state=closed" <br> $ curl -i "https://api.github.com/repos/vmg/redcarpet/issues?state=closed" <br> $ curl -i "https://api.github.com/repos/vmg/redcarpet/issues?state=closed" <br> </div>

Now this could be improved with a custom directive.