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

Interacting scalar field theory in $\kappa$-Minkowski spacetime