Positioning of the mitotic spindle is crucial for proper cell division. In the budding yeast Saccharomyces cerevisiae, two mechanisms contribute to spindle positioning. In the Kar9 pathway, astral microtubules emanating from the daughter-bound spindle pole body interact via the linker protein Kar9 with the myosin Myo2, which moves the microtubule along the actin cables towards the neck. In the dynein pathway, astral microtubules off-load dynein onto the cortical anchor protein Num1, which is followed by dynein pulling on the spindle. Yet, the mechanism by which microtubules target cortical anchor sites is unknown. Here we quantify the pivoting motion of astral microtubules around the spindle pole bodies, which occurs during spindle translocation towards the neck and through the neck. We show that this pivoting is largely driven by the Kar9 pathway. The microtubules emanating from the daughter-bound spindle pole body pivot faster than those at the mother-bound spindle pole body. The Kar9 pathway reduces the time needed for an astral microtubule inside the daughter cell to start pulling on the spindle. Thus, we propose a new role for microtubule pivoting: By pivoting around the spindle pole body, microtubules explore the space laterally, which helps them search for cortical anchor sites in the context of spindle positioning in budding yeast.