Yes, use the code:
wp_enqueue_script('tiny_mce');
This will include the TinyMCE javascript. Then simply use TinyMCE as you wish
<script type="text/javascript">
tinyMCE.init({
mode : "textareas",
theme : "advanced",
plugins : "autolink,lists,spellchecker,pagebreak,style,layer,table,save,advhr,advimage,advlink,emotions,iespell,inlinepopups,insertdatetime,preview,media,searchreplace,print,contextmenu,paste,directionality,fullscreen,noneditable,visualchars,nonbreaking,xhtmlxtras,template",
theme_advanced_buttons1 : "save,newdocument,|,bold,italic,underline,strikethrough,|,justifyleft,justifycenter,justifyright,justifyfull,|,styleselect,formatselect,fontselect,fontsizeselect",
theme_advanced_buttons2 : "cut,copy,paste,pastetext,pasteword,|,search,replace,|,bullist,numlist,|,outdent,indent,blockquote,|,undo,redo,|,link,unlink,anchor,image,cleanup,help,code,|,insertdate,inserttime,preview,|,forecolor,backcolor",
theme_advanced_buttons3 : "tablecontrols,|,hr,removeformat,visualaid,|,sub,sup,|,charmap,emotions,iespell,media,advhr,|,print,|,ltr,rtl,|,fullscreen",
theme_advanced_buttons4 : "insertlayer,moveforward,movebackward,absolute,|,styleprops,spellchecker,|,cite,abbr,acronym,del,ins,attribs,|,visualchars,nonbreaking,template,blockquote,pagebreak,|,insertfile,insertimage",
theme_advanced_toolbar_location : "top",
theme_advanced_toolbar_align : "left",
theme_advanced_statusbar_location : "bottom",
theme_advanced_resizing : true,
skin : "o2k7",
skin_variant : "silver",
});
</script>
You could also opt to use a WordPress plugin for TinyMCE, such as this TinyMCE plugin for WordPress, which is very popular.