X-ray imaging is a widely utilised non-destructive technique in both medical and industrial applications. Contemporary advancements, such as computed tomography (CT), enable the reconstruction of three-dimensional representations of internal structures from multiple projection angles. This study presents the development of a compact and functional CT system based on a portable X-ray source and a digital detector. A key component of the system is a custom-designed calibration phantom manufactured using 3D printing and incorporating precisely arranged steel spheres. Geometric calibration is performed using an iterative optimization approach based on sphere projections acquired from multiple viewing angles. The proposed method achieves sub-pixel calibration accuracy, with residual geometric deviations consistently below approximately one-fifth of a detector pixel. The impact of calibration is demonstrated by a clear reduction of geometry-induced artifacts and an improvement in reconstruction consistency compared to the uncalibrated case. The complete spatial configuration of the system, including source, object, and detector alignment, is explicitly described, enabling reproducibility and facilitating further development. The proposed setup supports reliable qualitative tomographic imaging with minimal hardware requirements, thereby promoting the wider adoption of mobile and cost-effective CT technologies for field and industrial applications.