In MVC doesn't have any control for datetime picker. So you should use jQuery UI datepicker or some other third party plugin. It's very easy to implement.
Download jquery plugin from here
http://jqueryui.com/download/[
^]
and then add the Scripts and css in head tag like below
<head>
<meta charset="utf-8">
<title>jQuery UI Datepicker - Default functionality</title>
<link rel="stylesheet" href="//code.jquery.com/ui/1.11.2/themes/smoothness/jquery-ui.css">
<script src="//code.jquery.com/jquery-1.10.2.js"></script>
<script src="//code.jquery.com/ui/1.11.2/jquery-ui.js"></script>
<link rel="stylesheet" href="/resources/demos/style.css">
<script>
$(function() {
$( "#datepicker" ).datepicker();
});
</script>
</head>
Also you should change your view code like below
<div class="editor-label">
<label for="studentDOB">
Date Of Birth</label>
</div>
<div class="editor-field">
@Html.TextBoxFor(model => model.studentDOB, new {id="datepicker"})
@Html.ValidationMessageFor(model => model.studentDOB)
</div>
Hope this helps