Reconfigurable intelligent surface (RIS) and ambient backscatter communication (AmBC) have been envisioned as two promising technologies due to their high transmission reliability as well as energy-efficiency. This paper investigates the secrecy performance of RIS assisted AmBC networks. New closed-form and asymptotic expressions of secrecy outage probability for RIS-AmBC networks are derived by taking into account both imperfect successive interference cancellation (ipSIC) and perfect SIC (pSIC) cases. On top of these, the secrecy diversity order of legitimate user is obtained in high signal-to-noise ratio region, which equals \emph{zero} and is proportional to the number of RIS elements for ipSIC and pSIC, respectively. The secrecy throughput and energy efficiency are further surveyed to evaluate the secure effectiveness of RIS-AmBC networks. Numerical results are provided to verify the accuracy of theoretical analyses and manifest that: i) The secrecy outage behavior of RIS-AmBC networks exceeds that of conventional AmBC networks; ii) Due to the mutual interference between direct and backscattering links, the number of RIS elements has an optimal value to minimise the secrecy system outage probability; and iii) Secrecy throughput and energy efficiency are strongly influenced by the reflecting coefficient and eavesdropper's wiretapping ability.