  In this short note we define a new cohomology for a Lie algebroid
$\mathcal{A}$, that we call the \emph{twisted cohomology} of $\mathcal{A}$ by
an odd cocycle $\theta$ in the Lie algebroid cohomology of $\mathcal{A}$. We
proof that this cohomology only depends on the Lie algebroid cohomology class
$[\theta]$ of the odd cocycle $\theta$. We give a few examples showing that
this new cohomology encompasses various well-known cohomology theories.
