  We construct slowly rotating black-hole solutions of Einsteinian cubic
gravity (ECG) in four dimensions with flat and AdS asymptotes. At leading order
in the rotation parameter, the only modification with respect to the static
case is the appearance of a non-vanishing $g_{t\phi}$ component. Similarly to
the static case, the order of the equation determining such component can be
reduced twice, giving rise to a second-order differential equation which can be
easily solved numerically as a function of the ECG coupling. We study how
various physical properties of the solutions are modified with respect to the
Einstein gravity case, including its angular velocity, photon sphere, photon
rings, shadow, and innermost stable circular orbits (in the case of timelike
geodesics).
