Nondestructive characterization is often carried out on dense materials and objects, such as cargo, and high atomic number advanced manufactured, and traditionally manufactured parts and assemblies. These often require high-energy x-rays, exceeding 1 MeV, and sub-millimeter spatial resolution for characterization. Current high-energy x-ray systems offer limited flexibility in tuning the x-ray energy and spatial resolution. Current x-ray sources include bremsstrahlung tube heads that operate from 10 to 600 kV and accelerators that operate from 2 to 15 MV. The MV systems have spatial resolution on the order of a millimeter which limits the features that can be observed. An alternative approach is to use an inverse Compton scattering (ICS) x-ray source with a linear plasma accelerator (LPA). This is a powerful emerging technology that can provide tunable keV to MeV, quasi-monoenergetic x-rays, and a focal spot size on the order of a micrometer. Our research seeks to answer the question: can ICS x-ray sources fundamentally change the way x-ray non-destructive characterization (NDC) is carried out on these challenging parts, assemblies, and cargo? We performed the first CT scans using the Berkeley Lab Laser Accelerator Hundred TeraWatt (BELLA HTW) ICS x-ray source. We scanned parts of tungsten carbide and steel. Our reconstructed images, although they have artifacts, demonstrate the potential of the LPA-ICS source to image challenging objects. We will discuss the system used, results, lessons learned and paths forward.