  We present a detailed analysis of a rotating black hole surrounded by
"quintessence". This solution represents a fluid with a constant equation of
state, $w$, which can for example describe an effective warm dark matter fluid
around a black hole. We clarify the conditions for the existence of such a
solution and study its structure by analyzing the existence of horizons as well
as the extremal case. We show that the deflection angle produced by the black
hole depends on the parameters $(c,w)$ which need to obey the condition $cw<0$
because of the weak energy condition, where $c$ is an additional parameter
describing the hair of the black hole. In this context, we found that for
$w\simeq 0.1$ (consistent with warm dark matter) and $c<0$, the deviation angle
is larger than that in the Kerr spacetime for direct and retrograde orbits. We
also derive an exact solution in the case of $w=-1/3$.
