But it would seem they weren't totally vestigial:

One of the biggest mysteries about T. rex has nagged palaeontologists for more than a century: what use did the giant have for arms so stubby that they could not even have reached its mouth? Early ideas, later discarded, suggested that the two-clawed arms helped T. rex to grip a partner during mating or to rise from repose. Later palaeontologists argued that the arms were vestigial — an idea beloved by cartoonists, who never tire of showing T. rex embarrassed by its useless, puny guns.

But research by palaeobiologist Sara Burch at Ohio University suggests that such jokes are unfair. She has studied the musculature of crocodylians as well as that of the only living members of the dinosaur line — birds. If the arms of T. rex had been vestigial, they would have lost the various anatomical landmarks that indicate muscle attachments, but the fossils “retain evidence of substantial musculature,” she says.

But knowing that T. rex used its arms doesn't reveal what they were used for. To Carr, the arms were part of the dinosaur's arsenal. “Tyrannosaurids used their arms in the same way all theropods used their arms, for grasping and stabilizing objects” — namely prey, he says.

Holtz visualizes a less rigorous role for the forelimbs. On the basis of previous estimates of muscle strength, he argues that T. rex had weak arms. And because many tyrannosaurs have arms with healed fractures, he says, “their life habits could not require constant use of these arms”. Holtz suggests that they were used primarily for display, perhaps during mating or competition— a possibility that seems more likely if these limbs were cloaked in feathers.