T. rex couldn't run fast, wasn't agile, and could not jump around or even fall down without doing serious damage or even dying. T. rex was too large to make agile movements required of an efficient predator. T. rex had no means of grasping or catching prey, and had very poor eye-sight. Carrion-eaters require massive bodies to scare off other potential carrion feeders or even the original predators. They also have a need for large heads so they can devour large volumes of food in very short periods of time.
Scavengers also require a tremendous sense of smell, to locate carrion.
T. rex has a huge head compared to its body and a massive body. In addition, T. rex had the best sense of smell of any dinosaur that ever lived on earth. Recently, a paleontologist at Berkeley demonstrated that T. rex had tremendous power in its bite, and that this power indicated T. rex to be a predator. As we all know, however, scavengers require more powerful jaws than do predators because carrion-feeders eat meat that is not fresh, and also crush bones. The reason is pretty simple.