Based upon your original html, you could do something like this:
Html:
<ul id="cat">
<li id="3">Text 3</li>
<li id="1">Text 1</li>
<li id="2">Text 2</li>
</ul>
JavaScript:
$("#cat li").sort(function (a, b) {
return parseInt(a.id) > parseInt(b.id);
}).each(function () {
var elem = $(this);
elem.remove();
$(elem).appendTo("#cat");
});
Check out this fiddle.
EDIT:
As @KiKo has correctly pointed out, the above code breaks if you have a list longer than ten elements. You can fix this by replacing the "greater than" in the sort function with a minus.
Html:
<ul id="cat">
<li id="3">Text 3</li>
<li id="2">Text 2</li>
<li id="1">Text 1</li>
<li id="9">Text 9</li>
<li id="11">Text 11</li>
<li id="5">Text 5</li>
<li id="7">Text 7</li>
<li id="6">Text 6</li>
<li id="12">Text 12</li>
<li id="4">Text 4</li>
<li id="10">Text 10</li>
<li id="8">Text 8</li>
</ul>
JavaScript:
$("#cat li").sort(function(a, b) {
return parseInt(a.id) - parseInt(b.id);
}).each(function() {
var elem = $(this);
elem.remove();
$(elem).appendTo("#cat");
});
Here's a new JSFiddle.