An attempt to answer this question was presented at the June 2005 Symposium "100 Years of Tyrannosaurus rex". Rex,Sit examines the question:
The challenge was to try to understand how Tyrannosaurus rex might have transitioned between a bipedal, standing posture and a resting pose. It has long been expected that the great theropod would have settled its weight upon its pubic boot. Just how might it have sat down and gotten up again?
In order to address the question:
The appendicular skeleton and head were digitized; the remainder of the axial skeleton was represented in a more schematic form, with important parameters (e.g., centrum length, neural spine height, and intervertebral separations) accurate based on measurements taken off of the specimen.
Two Quicktime movies were created based on this. One shows T. rex going from a standing to a sitting position and the other shows it rising from a sitting position. Unfortunately, I can't provide direct links to the movies so you will have to follow the link above. The movies are at the very bottom of the page.