Are there any Mexican-Americans on the US Supreme Court?

We currently do, yes (assuming you are referring to the United States Supreme Court). Her name is Sonia Sotomayor, and she was nominated by President Barack Obama; she has served on the Court since August 2009. She had previously served as a judge and lawyer in several other positions, and was best known for filing an injunction that ended the 1995 Major League Baseball Strike -- earning her praise from some for having "saved baseball."

Whether she is the first Hispanic justice actually sparked a brief discussion around the time of her nomination. A prior justice, Benjamin Cardozo, had been born to a family of Sephardic Jews originally from Portugal. The consensus, soon agreed upon, was that the term "Hispanic" must refer to someone whose heritage is in either Spain or Spanish-speaking Latin America. Under that definition, Brazilians would not be Hispanic, and neither would Cardozo. Thus, Sotomayor is the first.