Current endovascular therapies for intracranial aneurysms face limitations that include aneurysm recurrence and incomplete occlusion. These challenges can potentially be addressed by occluding the aneurysm space with shape memory polymers (SMPs) that are tailorable to patient‐specific aneurysm geometries to improve the suboptimal treatment outcomes associated with coil embolization. However, deployment of the SMP‐based device into the aneurysm requires external stimuli to trigger shape recovery. Thus, herein, the infiltration of carbon nanotubes (CNTs) in a polyurethane SMP foam is investigated, and Joule‐heating triggering for SMP shape recovery in endovascular therapy applications is demonstrated. The results show that CNTs can be successfully infiltrated in the SMP foam, providing tunable resistivity and shape recovery time, and that CNT infiltration reduces the glass transition temperature of the SMP and alters its mechanical properties, which is evidenced with a cumulative stress reduction in cyclic compression tests. Finally, the Joule‐heating capability of the SMP material is examined using a proof‐of‐concept in vitro occlusion experiment of an idealized saccular aneurysm model. Collectively, this study indicates that CNT infiltration of SMP foams is a promising approach in the design of electrically triggered embolic devices for individualized treatment of intracranial aneurysms.