  In this article we will use the Drinfeld twist leading to light-like
$\kappa$-deformations of Poincar\'e algebra. We shall apply the standard Hopf
algebra methods in order to define the star-product, which shall be used to
formulate a scalar field theory compatible with $\kappa$-Poincar\'e-Hopf
algebra. Using this approach we show that there is no problem with formulating
integration on $\kappa$-Minkowski space and no need for introducing a new
measure. We have shown that the $\star$-product obtained from this twist
enables us to define a free scalar field theory on $\kappa$-Minkowski space
that is equivalent to a commutative one on a usual Minkowski space. We also
discuss the interacting $\phi^4$ scalar field model compatible with
$\kappa$-Poincar\'e-Hopf algebra.
