Searching for recyclable materials of construction, in the objective of building sobriety and resilience, is a major issue of our current societies. Mudbricks of compacted rammed earth represent an ancient construction material with many advantages associated with its availability, cost of production, potential reuse, and with a very low carbon footprint. Moisture content affects the mechanical resistance of such materials, which could become mechanically weak above a critical value. Therefore, non-intrusive characterization techniques able to image the water content distribution of these materials is highly in demand. We apply a recently developed theory of complex electrical conductivity (alias induced polarization) to characterize core samples of rammed earth materials in the laboratory. Complex conductivity describes both the ability of a porous material to conduct an electrical current (characterized by the in-phase conductivity) and its ability to store reversibly electrical charges (characterized by two interconnected properties namely the quadrature conductivity and the normalized chargeability). Samples of rammed earth and clayey soils with different pore water salinities, saturations, and compaction states are measured with the complex conductivity method in the frequency range 100 mHz-45 kHz. The in-phase and quadrature conductivities of the complex conductivity of rammed earth are connected to the water content offering therefore a new non-intrusive tomographic technique to study the water content distribution in walls made of rammed earth. The data are all consistent with the so-called dynamic Stern layer model of complex conductivity for clayey materials. This new approach provides a general method to image the change in the water content of walls made of rammed earth, a task that electrical conductivity imaging cannot perform as a stand-alone technique.