  We study slowly rotating, asymptotically flat black holes in Einstein-aether
theory and show that solutions that are free from naked finite area
singularities form a two-parameter family. These parameters can be thought of
as the mass and angular momentum of the black hole, while there are no
independent aether charges. We also show that the aether has non-vanishing
vorticity throughout the spacetime, as a result of which there is no
hypersurface that resembles the universal horizon found in static, spherically
symmetric solutions. Moreover, for experimentally viable choices of the
coupling constants, the frame-dragging potential of our solutions only shows
percent-level deviations from the corresponding quantities in General
Relativity and Horava gravity. Finally, we uncover and discuss several
subtleties in the correspondence between Einstein-aether theory and Horava
gravity solutions in the $c_\omega\to\infty$ limit.
