  Hopf algebroid structures on the Weyl algebra (phase space) are presented. We
define the coproduct for the Weyl generators from Leibniz rule. The codomain of
the coproduct is modified in order to obtain an algebra structure. We use the
dual base to construct the target map and antipode. The notion of twist is
analyzed for $\kappa$-deformed phase space in Hopf algebroid setting. It is
outlined how the twist in the Hopf algebroid setting reproduces the full Hopf
algebra structure of $\kappa$-Poincar\'e algebra. Several examples of
realizations are worked out in details.
