You might want to use the HTML5 element:
<input file="type" />
For a more 'Angular-friendly' solution, you could try using the following library (which ultimately also uses the HTML5 input element): https://github.com/danialfarid/ng-file-upload
However, if you're looking for a native Cordova solution to access the file system, I'm stumped as well. That's something I'd like to know too. The problem is that using the HTML5 solution is pretty limited in terms of options.