Interesting thought but the immediate question is why would you want to? For the cost of whatever you could find, you can certainly upgrade your machine to a larger displacement one. The 570 is rated at 44HP. I doubt that Polaris engineered it to handle the added boost from a turbo. And I would be really surprised if anyone made a kit for a 570 since I don't think there is enough demand for it. So you would have to figure out what parts you needed and engineer everything from parts that are available off the shelf. Or have an aftermarket company design you a really expensive one off kit. And with the added air, you will have to get someone to write a tune for the ECU for timing and fuel delivery. Injectors might be a problem too.
Polaris does turbos on the 1000cc RZR which would be the same engine as the 1000 Sportsman and Scrambler so you might be able to start with the parts from that system.
Keep us posted if you do find something. I am intrigued by the idea!
Mine: 2018 Sportsman 850SP - 26" Bear Claw HTRs on OEM steel wheels(I really don't like the Aluminum ones)
Polaris Hand warmers, Mirrors.
Hers: 2007 Sportsman 500 EFI, Polaris Winch, 26" Bear Claw HTRs on Moose 427x Wheels. QSC Clutch Kit, Hand Warmers
2001 Magnum 325 MOSE 12" rear wheel conversion. 25" Sedona Coyote tires
2001 Magnum 325 Warn winch and Moose 60" plow
2017 Polaris Ranger 1000XP - Roof and front glass
SOLD 2004 Sportsman 600 Twin