When a star is tidally disrupted by a supermassive black hole (SMBH), the streams of liberated gas form an accretion disk after their return to pericenter. We demonstrate that Lense-Thirring precession in the spacetime around a rotating SMBH can produce significant time evolution of the disk angular momentum vector, due to both the periodic precession of the disk and the nonperiodic, differential precession of the bound debris streams. Jet precession and periodic modulation of disk luminosity are possible consequences. The persistence of the jetted x-ray emission in the Swift J164449.3+573451 flare suggests that the jet axis was aligned with the spin axis of the SMBH during this event.