The mechanisms by which the mammalian mitotic spindle is guided to a predefined orientation through microtubule-cortex interactions have recently received considerable interest, but there has been no dynamic model that describes spindle movements toward the preferred axis in human cells. Here, we develop a dynamic model based on stochastic activity of cues anisotropically positioned around the cortex of the mitotic cell and we show that the mitotic spindle does not reach equilibrium before chromosome segregation. Our model successfully captures the characteristic experimental behavior of noisy spindle rotation dynamics in human epithelial cells, including a weak underlying bias in the direction of rotation, suppression of motion close to the alignment axis, and the effect of the aspect ratio of the interphase cell shape in defining the final alignment axis. We predict that the force exerted per cue has a value that minimizes the deviation of the spindle from the predefined axis. The model has allowed us to systematically explore the parameter space around experimentally relevant configurations, and predict the mechanistic function of a number of established regulators of spindle orientation, highlighting how physical modeling of a noisy system can lead to functional biological understanding. We provide key insights into measurable parameters in live cells that can help distinguish between mechanisms of microtubule and cortical-cue interactions that jointly control the final orientation of the spindle.