You need to edit core WordPress file to achieve this.
Go to wp-includes folder of your wordpress directory and search for "widgets.php" file.
Open this file in normal txt editor and locate line number 1084 or search for string 'images/rss.png' .
Exactly below that line you will see following code,
$title = "<a class='rsswidget' href='$url' title='" . attribute_escape(__('Syndicate this content')) ."'><img style='background:orange;color:white;border:none;' width='14' height='14' src='$icon' alt='RSS' /></a> <a class='rsswidget' href='$link' title='$desc'>$title</a>";
Now delete first link from that variable. It should look line this after deletion,
$title = "<a class='rsswidget' href='$link' title='$desc'>$title</a>";
Save this file and we have done it. check your blog and you wont see that RSS feed icon.
Please keep this in mind that every time you upgrade your WordPress blog you need to edit this file also in future this file may get changed or code get modified then this hack will not work.