: Your question is a bit confusing. But I think I understand. I am going to make some assumptions. One is, you have a web server enabled, but no website. **Update: Okay, from the comments,

Your question is a bit confusing. But I think I understand. I am going to make some assumptions. One is, you have a web server enabled, but no website.

**Update: Okay, from the comments, your question is not clear at all. I am updating the answer to be more complete.

No. DNS stands for Domain Name Service. It translates domain names to routable IP addresses. Nothing more.

If you do not want snapshots of an empty site, you do not need a robots.txt file, you simply turn off the web server. By turn off, I mean stopping the service.

Here is the Apache documentation:
httpd.apache.org/docs/2.2/en/stopping.html
Here is a Microsoft page (may not be the latest):
technet.microsoft.com/en-us/library/cc732317(v=ws.10).aspx
If this is not what you want to do, then simply put up a robots.txt in your root, but make sure that either www redirects to mydomain.com or mydomain.com redirects to
# redirect root to www
RewriteCond %{HTTP_HOST} ^mydomain.com$ [NC]
RewriteRule ^(.*)$ www.mydomain.com/ [R=301,L]

Archive.org does a very poor job of respecting website owners wishes. There are holes in their processes and policies. For example, if your site disappears, archive snapshots can reappear. As well, it is very possible that archive.org see and obeys robots.txt via mydomain.com but not vie mydomain.com. Even when the robots.txt can be read either way, archive.org can ignore these and index your site anyway. Having said that, if all the stars align, archive.org can read the robots.txt file and drop all snapshots, but I have seen them come back months later.

Make sure you can access your robots.txt file from both mydomain.com and mydomain.com. This is important. Create the file and put an entry in it like this:

User-agent: ia_archiver
Disallow: /

If you cannot access your site as mydomain.com and mydomain.com, check your DNS server for the following:

An A record associating your IP address to mydomain.com
A CNAME record associating mydomain.com to mydomain.com
-or-
An A record associating your IP address to mydomain.com
I think this should do it. I can update more if it is required.