If I want to get a Ph.D. degree in the sciences from an American University, do I have to get first a Master's degree from the same University even if I already obtained it from another place?

Generally, if you have a degree, you have a degree.  Where the degree is from doesn't matter, all have similar levels of expectations to earn the degree in the first place.  There are of course exceptions, but in general.

You have a master degree is very important if you like to pursue the Ph.D in related field regardless of the country or the university in general.There are centers in USA to evaluate your degree and translate it if it is in different language. Each school in USA has its own criteria of evaluating students.The major is also vary from school to school interm of the rules of evaluations.My advice is to start as M.S in the same field you already earned your degree , in the mean time try to prove yourself to the school you applied to. Certainly the school and the advisor can look at your performance and they can merge your curriculum into the Ph.D program.You are the captain in your path to the future , it is fully in your hand , you can do it , if you are passionate enough about it , the sky is the limit to any passionate person regardless of the origin, sex, race, color, religion etc.Best Luck