At first glance, you might assume so and while many paleontologists agree it was a predator, I do not. Based on the preponderance of fossil evidence, it makes more sense that T. rex scavenged food for a living. Predatory animals require certain characteristics in order to be efficient killers. They need to be able to run fast and have the agility to quickly maneuver and leap.
Smaller animals are always more maneuverable than large animals.
Predators need to be capable of grasping and catching prey, and also require a good sense of sight. 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.