  In this paper, we study the shadow cast by two types of charged and slowly
rotating black holes in Eisntein-aether theory of gravity. This two types of
black holes are corresponding to two specific combinations of the coupling
constants of the aether field, i.e., $c_{14} = 0$ but $c_{123}\neq 0$ for the
first type and $c_{123} = 0$ for the second type, respectively. For both types
of black holes, in addition to the mass and charge of the black holes, we show
that the presence of the aether field can also affect the size of the shadow.
For the first type black hole, it is shown that the shadow size increases with
the parameter $c_{13}$, while for the second type black hole, the shadow size
still increases with c13 but decreases with the parameter $c_{14}$. With these
properties of these aether parameters, we also discuss the observational
constraints on these parameters by using the data of the first black hole image
by the Event Horizon Telescope. In addition, we also explore the effect of the
aether field on the the deflection angle of light and the time delay by using
the Gauss-Bonnet theorem. It is shown that, for a specific combination $c_{123}
= 0$, the deflection angle/time delay is slightly affected by the aether
parameter $c_{13}$ at the leading order.
