  This paper investigates Rota-Baxter associative algebras of of arbitrary
weights, that is, associative algebras endowed with Rota-Baxter operators of
arbitrary weights from an operadic viewpoint. Denote by $\RB$ the operad of
Rota-Baxter associative algebras. A homotopy cooperad is explicitly
constructed, which can be seen as the Koszul dual of $\RB$ as it is proven that
the cobar construction of this homotopy cooperad is exactly the minimal model
of $\RB$. This enables us to give the notion of homotopy Rota-Baxter
associative algebras. The deformation complex of a Rota-Baxter associative
algebra and the underlying $L_\infty$-algebra structure over it are exhibited
as well.
