What you need is a .pls file (just like the playlist files used in Winamp) to launch the stream. But instead of putting file names of MP3's in there, you put the like to your Shoutcast server. For example:
[playlist]
numberofentries=1
File1=http://yourserver.com:8000
Title1=Your Stream Title
Length1=-1
Version=2
The :8000 number on the end of File1 should be whatever port # you're using for your Shoutcast server (the default is 8000). Save the whole thing as a text file and name it something like stream.pls, upload it to your server and create a hyperlink on your webpage to the file. You also need to make sure you have the .pls extension registered on your web server as a valid mime type. I believe it's "audio/x-scpls pls" If not, when someone clicks on the link, the server will just send them the plaintext of the file which is not what you want.
Alternatively, you could just link directly to your Shoutcast server and let it handle the details, such as:
<a href="http://yourserver.com:8000/listen.pls">Click to listen</a>
Again replacing 8000 with whatever port # your Shoutcast server is running on. This way is a little easier because you don't have to deal with mime types. But you also lose the ability to link multiple servers with the same "Listen" link.