  We calculate the holographic entanglement entropy for the rotating
cylindrical black holes in $d+1$ dimensions as perturbations over $AdS_{d+1}$.
This is accomplished based on the first order variation of the area functional
in arbitrary dimensions. For these types of black holes, the angular momentum
appears at the first order of the perturbative expansion of the holographic
entanglement entropy for spacetime dimensions of d +1 $\geq$ 4. We obtain a
form of holographic entanglement first law in the presence of both energy and
angular momentum.
