  We construct an complex scalar field theory in $\kappa$-Minkowksi spacetime,
which respects $\kappa$-deformed Poincar\'e symmetry. One-loop calculation
shows that the theory is finite and needs finite renormalization to be
compatible with the $\kappa \to \infty$ limit. The loop result also has an
imaginary valued correction due to the complex poles present in the propagator.
