It was originally thought that the tyrannosaurus rex did stand upright like a kangaroo, as you mention. In fact, beginning in the 19th century, when the first complete skeletons of large bipeds were discovered, they were displayed standing at 45 degrees or even more acutely upright.

However, in the 1970's scientists discovered that the skeletal structure wouldn't have supported the t-rex standing upright and in fact the animal would have been non-functional if it did. In B.H. Newman's publication ''Stance and gait in the flesh-eating dinosaur Tyrannosaurus'' in 1970, he identifies that if the t-rex did stand upright it would have resulted in the dislocation or weakening of several joints, including the hips and articulation between the head and spinal column.

Although that would be cool (and very creepy for the T-rex's prey), I don't think so. If you look at the tail vertebrae of a kangaroo, you can tell that its tail is made to bend vertically for what you are describing. However, the tail vertebrae of a T-rex is built to bend horizontally for keeping balance. It is also much longer and less “sturdy” for lifting. Therefore, the bones would not be able to support the T's weight without breaking. What you must also take into consideration is the T's enormous and extremely heavy head in comparison to the small and lithe head of the kangaroo. The T leans forward because his head is so heavy and his tail balances him out and can be used for swinging side to side at his foe. If he were to stand upright, however, he would be in for some serious "back problems," so to speak, because his feet aren't really large enough in comparison to the rest of his body to bare that weight alone. Also, if you notice the pelvic structure of the kangaroo is made to swing on an axis for "kickboxing" whereas the T's is not. Hope this helps! =)

Kangaroo:
http://etc.usf.edu/clipart/12800/12833/kangaroo_12833_lg.gif
T-Rex:
http://www.enchantedlearning.com/tgifs/Trexskeleton.GIF