Amino acid conjugates are described by the reaction of amino acids with bioactive organic groups such as vitamins, hormones, flavonoids, steroids, and sugars. In this study, 12 new conjugates were synthesized by reaction of cinnamic acid derivatives with various amino acids. Cytotoxic studies against four different human cancer cells (MCF7, PC‐3, Caco‐2, and A2780) were carried out by MTT assay method at five different concentrations. The structure‐activity relationships based on the cell viability rates were evaluated. To compare the anticancer activities of the compounds using computational chemistry methods, they were docked against A2780 human ovarian cancer, Michigan Cancer Foundation‐7 (MCF7), human prostate cancer (PC‐3) and human colon epidermal adenocarcinoma (Caco‐2) cell lines and compared with the standard 5‐Fluorouracil. The results indicate that the efficacy of cinnamic acid derivatives increases with the presence of amino acids. Comet assay was conducted to understand whether the cell deaths occur through DNA damage mechanism and the results exhibit that the changes in the specified parameters were statistically significant (p<0.05). Our study demonstrated that the compounds cause cell death through the formation of DNA damage mechanism.