Yes. Under the United States Constitution, the Supreme Court has "original jurisdiction" (meaning it functions as a trial, rather than appellate, court) over disputes between the states. As you would imagine, most such disputes are handled not in court, but through agreements, often called "interstate compacts," which cover things like water rights. However, one state suing another in the Supreme Court is not unheard of, and the current water dispute between Tennessee, Georgia, and Florida may well be the next such case.
I would agree with the above answer. The only elaboration I would add is to explain that the U.S. Supreme Court's original jurisdiction stems from Article III, section 2, which provides in part that "In all cases affecting ambassadors, other public ministers and consuls, and those in which a state shall be party, the Supreme Court shall have original jurisdiction." If you are interested in learning more about this subject, I would direct you to examine all of Article III, section 2 and the cases which interpret it.