Change how the address bar shows for a website

I have a site that shows up as 123.123.123.123 (the ip that is used in binding)

I have my site sitting at c:\inetpub\wwwroot\website

Is it possible for my to set the site to automatically show up as 123.123.123.123/Thesite

Can I do this without moving my current c:\inetpub\wwwroot\website directory ?

thanks,