Yes you can! While you can roll with them as plug and play, it's not quite recommended. PS4 controllers don't quite work like Xbox 360 controllers, which SK is built to work with. Therefore, it's recommended to use a so called wrapper. A wrapper takes input from the PS4 controller and turns it into virtual Xbox 360 controller input, eliminating issues caused by the bad support for PS4 controllers.

I've been using a DS4 for almost a year and it's the best controller I've ever used for SK (compared to Xbox 360 controller and Wiimote+Nunchuck). I use DS4Windows, and it works pretty well. It also allows for various forms of customisation. You can, for example, bind your PS button to something else. I use mine to bring up the map.