Is there a way to stop google and other search engines searching my Google Sites website? Is there any robots.txt?
robots.txt of Google Sites is not user-editable. https://productforums.google.com/forum/#!topic/sites/E4lCgoEv6yw
Instead, you can use Google Search Console (a.k.a. Webmaster Tools) to remove your site from Google results. For more information see "How to remove your website or web page from Google". The tool's layout has since changed, but once you log in to the tool, you can still find "Remove URLs" under the heading "Google Index".
In the New Google Sites, you can do that:
Opt your site out of search engines
Important: This is a request and doesn’t guarantee that your site won’t show up in public search engines.
This option is only available if your site is set to "Public on the web," and can be viewed by anyone.
- On a computer, open a site in New Google Sites.
- At the top, next to "Publish," click the Down arrow.
- Click Publish settings.
- Click Request public search engines to not display my site.
- Click Save.