The first thing that comes to mind is that they were vestigial, that is, that they served no purpose and that evolution was gradually eliminating them, like the rear leg bones of whales. But this explanation does not hold up. First, these “arms” were only small in relation to the total size of the beast. They were actually about the size of a strong man’s arms, and it is calculated they were probably muscular enough to bench press 400 lbs.
The small forelegs were also not just peculiar to T.Rex itself. Many of its evolutionary ancestors, such as Allosaurus, also were built on the same plan–massive rear legs and tiny front ones. These genetic cousins were spread out over millions of years, all over the planet, and were of many different sizes. Surely, this design feature was not just a rapidly vanishing afterthought. T. Rex was one of the last dinosaurs to disappear at the end of the Cretaceous. By the time evolution got around to him, purely vestigial front legs should have long ago disappeared. No, these tiny forelimbs were a vital part of the design of an entire family of dinosaurs.
Paleontologists freely admit they don’t know why these tiny forearms existed, or their purpose. Modern flightless birds, creatures who probably moved a lot like dinosaurs, don’t have any analogous structures. It has been suggested they were used to handle small game, to carry pieces of prey back to the nest, to transport or rearrange nesting material, to carry young or eggs, or they served some purpose in courting or in inter-species communication. It has even been argued they helped the animal leverage itself back on its feet from a prone position. None of these explanations seem very convincing, and none sound critical enough that this feature was repeated across so many different related organisms.