Microtubules and actin filaments function coordinately in many cellular processes(1-3). Although much of this coordination is mediated by proteins that statically bridge the two cytoskeletal networks(4-6), kinesin-14 motors with an actin binding calponin homology domain (KCHs) have been discovered as putatively dynamic crosslinkers in plants(7,8). OsKCH1, a KCH from rice, interacts with both microtubules and actin filaments in vivo and in vitro(9). However, it has remained unclear whether this interaction is dynamic or if actin binding reduces or even abolishes the motor's motility on microtubules(10,11). Here, we directly show in vitro that OsKCH1 is a non-processive, minus-end-directed motor that transports actin filaments along microtubules. Interestingly, we observe two distinct transport velocities dependent on the relative orientation of the actin filaments with respect to the microtubules. In addition, torsional compliance measurements on individual molecules reveal low flexibility in OsKCH1. We suggest that the orientation-dependent transport velocities emerge from OsKCH1's low torsional compliance combined with an inherently oriented binding to the actin filament. Together, our results imply a central role of OsKCH1 in the polar orientation of actin filaments along microtubules, and thus a contribution to the organization of the cytoskeletal architecture.