My immediate thought is that you are too worried about school and not worried enough about your career. PhDs and JDs lead in completely different directions - the schooling itself is the least of it. What kind of PhD are we talking about here? What do you want to do after finishing school, whether grad school or law school?
If that deliberation leads you towards law school, I offer this insight as well: getting in to law school is not your problem as an international student - getting a job after graduation, that is your problem as an international student. Ignoring for the moment the current market conditions for lawyers in general, many of the attractive legal employers are not familiar with immigration practicalities, and will give you a puzzled look when you ask them to sponsor you for an H-1B. And green card? Triple ugh.
It varies significantly by field, of course, but I suspect that most employers in the market for PhDs will be far more friendly to immigrants than legal employers. That is assuming that you plan on staying here after graduation, of course - if that is not the case, then the decision is easy as law school would simply be foolish.
Transitioning from school to workforce is very difficult for international students in the US under any circumstance (unless you were to, say, fall and love and get married to an American citizen, of course...), but it may be more difficult for lawyers than for most.
As always, however, my main advice is to make your decisions based not on "now" but on "later." Determine your goals, and then make decisions that point you in the right direction.