I'm no expert, but I think you'll have to get an American degree if you'd like to practice in the US. Your current schooling will give you a bachelors, and most foreign lawyers come to the US to get a Masters of Law (LLM). If this is the path you'd like to take, you should know that it is very, very expensive. Although the programs are only 1yr long, the tuition can be as much as $80,000.
You should also think about where you would like to practice. To practice in the US, you must be admitted to a state bar (basically you take a difficult test that is often unique to each state). Each state has different requirements as to who can take the bar. For example, if you wanted to practice in New Jersey, you'd have to get an American JD first. In contrast, to practice in New York, all you need to do is take a few classes at a law school (usually accomplished by getting a LLM).
For now, here's what you should do/think about:
- Get very good marks at your current university
- Start saving up money if you can
- Think about where you would want to live in the US
