The focus of this research is an investigation on the fatigue behaviour of unidirectional 3D-printed continuous carbon fibre-reinforced polymer (CFRP) tension straps with a polyamide matrix (PA12). Conventionally produced tension straps are becoming established components in the mechanical as well as the civil engineering sector, e.g., as rigging systems for sailing boats and cranes and—recently introduced—as network arch bridge hangers. All these structures are subjected to high fatigue loads, and although it is commonly reported that carbon fibre-reinforced polymers show excellent fatigue resistance, there is limited understanding of the behaviour of CFRP loop elements under such loads, especially in combination with fretting at the attachment points. Research on this topic was performed at Empa in the past decade on thermoset CFRP straps, but never before with 3D-printed continuous CFRP straps with a thermoplastic matrix. This paper examines an additive manufacturing and post-consolidation method for producing the straps and presents initial results on their fatigue performance, which show that the fatigue endurance limit of the investigated 3D-printed and post-consolidated CFRP strap design is acceptable, when compared to steel tendons. However, it is still 20% lower than conventionally produced CFRP straps using out-of-autoclave unidirectional carbon fibre prepregs. The reasons for these findings and potential future improvements are discussed.