Solution:
There is WordPress plug-in called JSON-API it gives you ability to access every object of WordPress( post ,page ,category.. etc ) in the form of JSON. you can use any rest client like volley from google, retrofit from Square or build your won to access wordpress data.
install WordPress plug-in http://wordpress.org/plugins/json-api/
for sample code you can look WordPress for android source code on github https://github.com/wordpress-mobile/WordPress-Android