Yes. The best program I think is "Chess for Android". Make sure you get the one by the developer Jeroen Carolus. He has implemented many things I asked for in the past, like the ability to start from a specific start position by number, being able to save Chess960 games in PGN and I think he might be trying to enable online Chess960 as well. The program can use an external engine (as well as there being an inbuilt engine he wrote). I play using the latest Stockfish and set it to limited depth to reduce it's playing strength.
Jeroen has also resisted the temptation to put in advertising so support his program!
Is it possible to play chess 960 in the program for Android. Play between me and the computer? Or I can only play against real opponents online?