No. Tiger sharks are carnivores, although they are famous for having one of the least selective diets of any shark. They are ambush predators and scavengers whose prey commonly includes sea turtles, rays, other sharks, bony fishes, sea birds, dolphins, squid, crustaceans, and carrion.
Their reputation for eating almost anything comes from the non-food items found in their stomachs, such as cans, plastic bottles, and burlap sacks swallowed in harbors and river inlets. Those objects are swallowed by accident while scavenging; they are not a plant-based part of the diet, which is what would make an animal an omnivore.
Source: Florida Museum of Natural History: Tiger Shark (Galeocerdo cuvier)
Image: Tiger shark, Albert Kok, CC BY-SA 3.0, via Wikimedia Commons.