Yes. In fact, the Unites States has many laws that offer incentives to foreign investors.
All you need to start day trading is a computer and an Internet connection. Through the Internet, you can trade from any part of the world. That is one of the greatest advantages of having a trading business. No matter where you are or where you go, as long as you have access to the web, you can run your business.
What I do recommend is that you try to trade through a broadband (DSL or Cable Modem) connection or a fiber optic connection rather than through a dial-up connection (56Kbps), no matter which country you are trading from. In the last few years, I have worked with more investors and professional traders from non-US countries than from the United States.
Learn about day trading by first reading my 7 steps.