In this study, a comprehensive investigation was conducted to determine the radioactivity levels of naturally occurring radioactive materials (NORMs) in heap pads/soil and water samples within and around the operational area of Tarkwa Gold Mine in Ghana. Gamma-ray spectrometry was used to determine the activity concentrations of 238U, 232Th, and 40K in heap pads/soil, and 226Ra, 228Th, and 40K in water samples. The average activity concentrations of 226Ra and 228Th in all water samples were below the World Health Organisation (WHO) recommended guidelines for drinking water. Similarly, the average activity concentrations of measured radionuclides in heap pads/soil samples taken from depths of 0–20 cm and 20–50 cm were found to be below the worldwide average reported values. The annual effective dose to the public was estimated to be around 0.16 mSv, which is below the recommended limit. The values of the hazard indices are also below the recommended limits, implying that if heap pads/soils are used for building purposes and construction, they will not pose any significant radiation hazard. The results of this study indicate that radiation levels are within the natural background radiation levels reported in the literature and are consistent with findings from similar studies conducted in Ghana.