Acrylonitrile‐EPDM‐styrene (AES) was applied as an impact modifier for poly(lactic acid) (PLA), and the combined effect of dicumyl peroxide (DCP) crosslinking and annealing heat treatment was investigated. Torque rheometry, melt flow index (MFI), mechanical properties (impact, tensile, and Shore D hardness), X‐ray diffraction (XRD), infrared spectroscopy (FTIR), heat deflection temperature (HDT), differential scanning calorimetry (DSC), and scanning electron microscopy (SEM) were investigated. There was a considerable torque increment and fluidity drop in the PLA/AES/DCP blends caused by the crosslinking process and the formation of PLA‐g‐AES. Consequently, the impact strength and elongation at break properties improved. As an engineering terpolymer, AES was decisive in maintaining high elastic modulus, Shore D hardness, and HDT values. The PLA/AES/DCP (0.8 phr) composition leaned towards a synergism of mechanical properties, gaining 505.6% and 264.8% in impact strength and elongation at break, respectively, compared to neat PLA. FTIR and XRD analysis revealed high crystallinity, with samples presenting large crystals. The higher crystallinity had a deleterious effect on the mechanical properties of the PLA/AES/DCP blends. However, there was a marked improvement in HDT and higher toughness compared to PLA. The results before and after annealing the PLA/AES/DCP (0.8 phr) blend are promising for constructing new semi‐biodegradable materials for additive manufacturing.