Backscatter communication (BC) has emerged as a pivotal wireless communication paradigm owing to its low-power and cost-effective characteristics. However, BC faces various challenges from its low signal detection rate to its security vulnerabilities. Recently, reconfigurable intelligent surfaces (RIS) have surfaced as a transformative technology addressing power and communication performance issues in BC. However, the potential of RIS in addressing the security challenges of BC remains uncharted. This paper investigates the secrecy performance of RIS-aided BC, where all channels are distributed according to the Fisher-Snedecor $\mathcal{F}$ distribution. Specifically, we consider a RIS with $N$ reflecting elements to help a backscatter device (BD) establish a smart environment and enhance the secrecy performance in BC. Due to the nature of BC systems, our analysis considers two possible scenarios (i) in the absence of direct links and (ii) in the presence of direct links. In both cases, we first derive compact analytical expressions of the probability density function (PDF) and cumulative distribution function (CDF) for the received signal-to-noise ratio (SNR) at both a legitimate receiver and an eavesdropper. Then, to analyze the secrecy performance, we further derive analytical expressions of the average secrecy capacity (ASC) and secrecy outage probability (SOP) for both mentioned scenarios. In addition, regarding the importance of system behavior in a high SNR regime, we provide an asymptotic analysis of the SOP and ASC. Eventually, the Monte-Carlo simulation is used to validate the analytical results, revealing that utilizing RIS can greatly improve the secrecy performance of the BC system relative to traditional BC setups that do not incorporate RIS.