I had someone ask me how to do this the other day and I didn’t know how. But after reading through some of the WordPress Codex I was able to figure it out. To exclude specific categories from your RSS feed just add the following code snippet to your theme’s functions.php file.

function myFeedExcluder($query) {
 if ($query->is_feed) {
   $query->set('cat','-12');
 }
return $query;
}
add_filter('pre_get_posts','myFeedExcluder');

As always, make sure it is between PHP tags. And if the theme you are using does not have a functions.php file, just create on yourself and add the above code snippet after an opening PHP tag.