Date popup in exposed filter
The Better Exposed Filters module integrates with the date type fields, including the date popup. You can use this module to easily add an exposed filter with the date popup.

There are some known issues with BEF's integration with the date module; from the module page:


  (Note: Support for fields supplied by the Date module is a little funky until #392836: Exposed Date filter format (in Views) and/or #502824: Date format in exposed filter (views) are resolved).


Also, you can only add this type of filter to entity fields at the moment, not properties. There are various discussions going on about this.