You sure can! You can put a turbo on anything these days. The TRD turbo's will definitely work with scion's as they are powered by toyota engines. One thing to consider when ordering your TRD turbo from the toyota dealership is that it is not a bolt on and go thing. You will have to consider tuning your car's computer (ECU) and may need to get a modified MAF sensor. The amount of a TRD turbo kit can cost more than other brands such as HKS, Blitz, Greddy, to name a few, but have less power gains. Also depending on the amount of boost you want to run, you may require modifying your engine internals so it may handle the pressures of the boost, and also may need a stronger clutch. So the things to consider when buying a turbo are cost options of other brands, whether the TRD turbo kit includes all components - exhaust manifold, intercooler, intercooler piping, wastegate, blow off valves, boost guages, tuned ecu, and any necessary wiring needed.
Another option to consider is getting a supercharger. They are a safer option for a bolt on power as you dont have to worry about engine internals as much with a bolt on kit, and tuning is not such a headache. Greddy makes an awesome supercharger kit that includes everything including tuned ecu that is straight bolt on. Check out greddy.com and see the possible options for turbos and superchargers.