A heterogeneous solid acid catalyst was synthesized using tire polymer waste (TPW) for the esterification of waste chicken fat (CF) enriched with fatty acids. The TPW was carbonized and functionalized with concentrated sulfuric acid under various sulfonation conditions to obtain a sulfonated tire polymer char (TPC-SO3H) catalyst. The TPC-SO3H catalyst was further characterized via acid-base titration (to ascertain the total concentration of acid), X-ray diffraction, scanning electron microscopy (SEM), energy dispersive X-ray analysis (EDAX), and Brunauer–Emmett–Teller (BET) analysis. The esterification reaction conditions of extracted chicken fat with methanol and the viability of catalyst reuse were also investigated. The composition of the free fatty acid (FFA) decreased to below 1% under optimum reaction conditions of 5% TPC-SO3H catalyst, the methanol-to-CF molar-ratio of 15:1, and a reaction time of 120 min at 70 °C. The catalyst preserved its conversion efficiency above 90%, even after three cycles. The results demonstrate that the catalyst is applicable and efficient in the esterification of raw materials containing various fatty acid compositions since different carbonized materials have distinct abilities to combine acid groups. Furthermore, after de-acidification of CF-FFA by the as-prepared TPC-SO3H catalyst, the neutral CF was transesterified completely to biodiesel and characterized via Fourier Transform Infrared (FTIR) spectroscopy, proton nuclear magnetic resonance (1H NMR) spectroscopy and physicochemical analysis. This work unveils a promising technique for utilizing tire waste generated in large quantities for the development of a novel heterogeneous acid catalyst for biodiesel production.