Is it possible to control a game with an Android phone without Unity?

I mean, is it possible to create a game on PC with a Socket server and control the character on the game, through an wi-fi connection, with an Android phone, using an app designed for it (withou Unity for Android)?

Yes.

You can make use of System.Net.Sockets.Socket in Unity3D. Android is probably capable of connecting to another ip/port over TCPIP and at the very least you can make use of web posts.