Green chemistry methods for production of nanoparticles have many advantages, such as ease of use, which makes the methods desirable and economically viable. The aim of the present work was to green synthesise silver nanoparticles (SNPs) using aqueous tangerine peel extract in different ratios (2:1, 1:1, 1:2). The formed SNPs were characterised using ultraviolet-visible (UV-Vis) spectrophotometry, and transmission electron microscopy (TEM). The UV-Vis spectra showed that the highest absorbance was observed when the ratio of peel tangerine extract to silver nitrate solution was 1:2. The transmission electron micrographs showed the formation of poly dispersed nanoparticles. It was found that the average diameter of the nanoparticles was 30.29 ± 5.1 nm, 16.68 ± 5.7 nm, and 25.85 ± 8.4 nm, using a tangerine peel solution and silver nitrate solution ratio of 2:1, 1:1, and 1:2, respectively. The formed SNPs were evaluated as catalysts for methyl orange dye degradation, and the results confirmed that SNPs can speed up the degradation of the dye.