In the Divi Theme Documentation, it says that the theme comes with access to 'ePanel' which also has an 'Integration' section.
You should be able to add this code:
<script>
$( ".et-pb-icon" ).click(function() {
$( this ).toggleClass( "active" );
});
</script>
into the the box that says 'Add code to the head of your blog' under the 'Integration' tab, which should get the jQuery working.
Then, you should be able to style your class to what ever you need.