  Accretion disks in binary systems can exhibit a tilt instability, arising
from the interaction between components of the tidal potential and dissipation.
Using a linear analysis, we show that the aspect ratios and outer radii of
circumplanetary disks provide favorable conditions for tilt growth. We quantify
the growth rate of the instability using particle-based ({\sc phantom}) and
grid-based ({\sc athena++}) hydrodynamic simulations. For a disk with outer
aspect ratio $H/r \simeq 0.1$, initially moderate tilts double on a time scale
of about 15-30 binary orbits. Our results imply that detached circumplanetary
disks, whose evolution is not entirely controlled by accretion from the
circumstellar disk, may commonly be misaligned to the planetary orbital plane.
We discuss implications for planetary spin evolution, and possible interactions
between the tilt instability and Kozai-Lidov dynamics.
