I haven't tested this properly so I'm not sure how well it works in game. There is now support for the PS4 controller. it functions exactly like a Xbox One/Xbox 360 controller would except for the DPAD. You will have to go into the Steam Controller Configuration settings and tell the PS4 controller to make the DPAD act as the Left Stick. That should get it working.
Also while the PS4 controller is plugged in keyboard prompts will show up on screen. I will look into fixing that and update the game to show proper button prompts.