  Real astronomical objects possess spin, yet deriving exact solutions for
rotating black holes within gravitational theories is a formidable challenge.
To understand the shadow of rotating black holes in Lorentz-violating
spacetimes induced by antisymmetric tensor fields, known as Kalb-Ramond (KR)
fields, we have focused on the slow-rotation approximation framework. Using
this approach, we have obtained first-order rotation series solutions, which
describe slowly rotating KR black holes. For this solutions, we have plotted
the black hole shadow contours under various parameters using the numerical
backward ray-tracing method. As the Lorentz-violating parameter increases, not
only the apparent size of the black hole shadow decreases, but also the effects
of rotation, such as the D-shaped structure and frame-dragging, are amplified.
Furthermore, the KR field also enhances gravitational lensing, causing the
shadow to occupy a larger area within the photon ring. This distinctive feature
can differentiate KR gravity from general relativity. Additionally, using the
latest observational data from EHT on M87* and Sgr A*, we have provided
constraints on the Lorentz-violating parameter of rotating KR black holes. We
found that, compared to static black holes, rotating black holes allow for the
presence of stronger Lorentz violation effects.
