Yes, there are many tournaments, both small and large, local and international. Search for your home state to see specific locations and dates and qualification requirements.
If you mean Slalom ski you can go to INTleague.com and they have great competitions for all skill levels during the summers in virtaully every area of the United States.
I was one of the first Americans in the world to water ski and I learned from the person who conceived the sport. I can tell the story to anyone interested and it started in Europe at the end of...