SharePoint 2013 Tip of the Day – To have the drag and drop feature work in SharePoint 2013, here are the scenario or requirements of Web browsers.
Internet Explorer 10
Internet Explorer 9 with Office 2013 Installed
Internet Explorer 8 with Office 2013 Installed
FireFox latest version
Chrome latest version
Hence, for IE 8 and IE 9, it must have Office 2013 installed on the machines, else the drag and drop feature will not be available.