You have a few options for FPS like controls on a mobile device with the most common being twin joystick controls. One mapping to moving forward, back, and strafing left/right. The other for camera look.
I tried adding dual virtual sticks to my ‘Doom 3: Gangnam Style’ project a long time ago. I wouldn’t say it’s a nice, clean implementation, but hey, you might find it interesting to look at for inspiration.