Jan Henrik wrote this Instructables demonstrating how to program an Arduino with Android device:
in this Instructable I want to show you, how you can program your Arduino with your Android device. It is very simple and cheap. Also it allows us to program our Arduino where ever we want, this is usefull for permanently installed Arduino boards, like in light controllers…
I need to have information on how to program the Arduino with Android via WiFi communication
Well, I’m just starting to look at programming an Arduino Uno R3 using Android 4.2.2. ArduinoDroid (search on GooglePlay) which looks like a good candidate app, I think a simple solution would be to upload your Arduino code (.ino sketch) to the Android device via FTP then as a next step program the Arduino using the uploaded file with AndrodDroid. There are plenty of FTP host apps available for Android. I use the “Solid Explorer” file manager app (again see GooglePlay) that has a built-in FTP server.
Caveat, I have not tried this yet so YMMV… Let us know if this helps.