Rhus coriaria L. (sumac) is an important plant for both its recognized use as a spice and as a rich source for bioactive compounds. However, its phytochemical profile is sensitive to climate factors of its geographical location, making quality standardization a major challenge. This research therefore aims to quantify the effect of climate variables (altitude, temperature, and precipitation) of different geographical locations on the chemical makeup of sumac. Additionally, it aims to provide climate-calibrated multivariate chemometric discrimination of the fruits from different locations based on selected physicochemical traits. For this purpose, 80 mature fruit samples of sumac collected from 16 geographically distinct locations across the Kurdistan Region of Iraq were analyzed for eight quality markers: refractive index (RI), pH, titratable acidity (TA), electrical conductivity (EC), total dissolved solids (TDS), oxidation–reduction potential (ORP), total phenolic content (TPC), and radical-scavenging activity (RSA). Multivariate analysis employing principal component analysis (PCA) reduced the data to two components that explain 89.7% of total variance: PC1 (70.3%) separates low-temperature, high-altitude sites (high pH, low TA, EC, TDS, and ORP) from lower altitude locations (low pH, high TA, EC, TDS, and ORP), while PC2 (19.4%) orders samples along an altitude-driven phenolic gradient. Hierarchical clustering analysis (HCA) yielded four main clusters that coincide with altitude and temperature gradient, confirming geographical discrimination. Temperature is the dominant quantitative driver for seven of the eight traits (p ≤ 0.007), while precipitation modulates bioactive traits, and altitude contributes through interactions. The study provides the first quantitative climate–chemistry map for Kurdish sumac and a chemometric tool for geographical discrimination and selection of optimum environmental conditions.