Well I figured it after several hours of trial and error. I hope I can make someones day who comes searching in the future.
Put the following code into the header section of code injection
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script>
<script>
$( document ).ready(function() {
$( ".header-actions-action.header-actions-action--social" ).append("<div class='ec-cart-widget'></div>");
});
</script>
and then a bit of css to make the bag the same size as the other icons and change the color to be the same.
.ec-minicart--no-shape{
padding: 0px !important;
}
.ec-minicart__icon{
height: 30px !important;
width: 30px !important;
}
.ec-minicart__icon .icon-default path[stroke], .ec-minicart__icon .icon-default circle[stroke]{
stroke: #(color code you want) !important;
}
