Advances in synthetic biology have led to the design of biological parts that can be assembled in different ways to perform specific functions. For example, genetic circuits can be designed to execute specific therapeutic functions, including gene therapy or targeted detection and the destruction of invading viruses. Viral infections are difficult to manage through drug treatment. Due to their high mutation rates and their ability to hijack the host’s ribosomes to make viral proteins, very few therapeutic options are available. One approach to addressing this problem is to disrupt the process of converting viral RNA into proteins, thereby disrupting the mechanism for assembling new viral particles that could infect other cells. This can be done by ensuring precise control over the abundance of viral RNA (vRNA) inside host cells by designing biological circuits to target vRNA for degradation. RNA-binding proteins (RBPs) have become important biological devices in regulating RNA processing. Incorporating naturally upregulated RBPs into a gene circuit could be advantageous because such a circuit could mimic the natural pathway for RNA degradation. This review highlights the process of viral RNA degradation and different approaches to designing genetic circuits. We also provide a customizable template for designing genetic circuits that utilize RBPs as transcription activators for viral RNA degradation, with the overall goal of taking advantage of the natural functions of RBPs in host cells to activate targeted viral RNA degradation.