The T. Rex started out bipedal, with functional arms -- you can pick that as its starting point, there are plenty of those guys running around in the fossil record. As its head got bigger and bigger, it became top-heavy: its back end had to balance its front end when running, or else it would just face plant constantly.
If I had to guess (I haven't actually looked into how much of this we have recovered from the fossil record; I just happen to have heard the reason above) the T. Rex's head probably got pretty big first -- for a while, bigger heads could be counterbalanced by bigger tails while still retaining normal-sized arms. But there's a limit to how big animals can get, so eventually the proto-T. Rex would have the biggest tail it could support.
By this point it would be firmly in the big head niche: its diet, survival strategy, and sexual selection would revolve around using its giant head and powerful mouth to just bite the crap out of everything and generally be awesome. Now come the tiny arms: even when its arms were still functional, they were less awesome than its giant head. Trading slightly smaller, slightly less functional arms for a slightly gianter, slightly more awesome head was a win at every point down the curve, until it was stuck with tiny, useless arms and a really awesome head.
Their common ancestors may have evolved bipedalism because forelimbs proved cumbersome when taking down large prey.