We cannot exactly replicate the other website but still i have created this much.
HTML
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title></title>
    <script src="https://ajax.googleapis.com/ajax/libs/jquery/1.6/jquery.min.js" type="text/javascript"></script>
    <script src="https://ajax.googleapis.com/ajax/libs/jqueryui/1.8/jquery-ui.min.js"
        type="text/javascript"></script>
    <link href="https://ajax.googleapis.com/ajax/libs/jqueryui/1.8/themes/base/jquery-ui.css"
        rel="Stylesheet" type="text/css" />
    <script type="text/javascript">
        $(function () {
            $('#txtDate').datepicker({
                dateFormat: "dd/MM/yy",
                changeMonth: true,
                changeYear: true
            });
        });
    </script>
    <style type="text/css">
        body
        {
            font-family: Arial;
            font-size: 10pt;
        }
        #txtDate
        {
            background-image: url(https://i.imgur.com/u6upaAs.png);
            background-repeat: no-repeat;
            padding-left: 25px;
        }
    </style>
</head>
<body>
    <form id="form1" runat="server">
    <div>
        <input id="txtDate" type="text" name="name" />
    </div>
    </form>
</body>
</html>
 
Demo