Transfer factors (TFs) are widely used tools for assessing the uptake of radionuclides by plants. The literature contains numerous studies on TFs in tropical and temperate climates; however, the existing data on TFs in arid and semi-arid climates are very scarce. Furthermore, the current trend in nuclear energy expansion in countries with this type of climate necessitates knowledge of the mechanisms of radionuclide incorporation by plants as well as the TF values. For this reason, this work investigates the TFs of 238U and 226Ra in plants in a study area during the summer period under conditions equivalent to a semi-arid climate. The selected plants were Scolymus hispanicus L., Eryngium campestre L., Chenopodium vulvaria L., and Chenopodium album L., which were collected in the vicinity of a waste dump from an abandoned copper mine. The selected study area has radionuclide levels above the global average, in addition to heavy metals, as it is a waste dump from an abandoned copper mine. The range of transfer factors for 238U varied between 1.5 × 10−4 kg−1 kg−1 and 7.8 × 10−3 kg−1 kg−1, while for 226Ra, the range was between 1.8 × 10−4 kg−1 kg−1 and 4.0 × 10−2 kg−1 kg−1. The correlations found with PCA were (i) 238U with Fe and Al, and (ii) 226Ra with S, Ti, Ca, and Sr. A transfer model of 238U and 226Ra was created using multiple linear regression analysis. The model showed how 238U was related to the presence of Al, while 226Ra was related to Al, Fe, and Ti. The results obtained have allowed us to propose a model for the incorporation of 238U and 226Ra, taking into account the chemical composition of the soil. The results obtained indicate that both Scolymus hispanicus L. and Eryngium campestre L. could be utilized in phytoremediation for soils contaminated by natural radionuclides in semi-arid climates. The TFs, as well as the proposed model, allow us to expand the knowledge of the absorption of natural radionuclides by plants in regions with arid and semi-arid climates, which is necessary for the radiological risk assessment of future nuclear fuel cycle facilities.