Surface-swimming nano- and micromotors hold significant potential for on-chip mixing, flow generation, sample manipulation, and microrobotics. Here we describe rotating microrods magnetized nearly orthogonally to their long axes. When actuated near a solid surface, these microrods demonstrate precessing motion, with rods describing a double cone similar to the motion of a kayaker's paddle. The precessing motion induces translation. At 1 kHz, these "microkayaks" move at translational velocities of ≈14 μm s-1 and generate advective flows up to 10 μm s-1.