A synthetic approach to biology is a promising technique for various applications. Recent advancements have demonstrated the feasibility of constructing synthetic two-input logic gates in Escherichia coli cells with long-term memory based on DNA inversion induced by recombinases. On the other hand, recent evidences indicate that DNA inversion mediated by genome editing tools is possible; powerful genome editing technologies, such as CRISPR-Cas9 systems, have great potential to be exploited to implement large-scale recombinase-based circuits. What remains unclear is how to construct arbitrary Boolean functions based on these emerging technologies. In this paper, we lay the theoretical foundation formalizing the connection between recombinase-based genetic circuits and Boolean functions. It enables systematic construction of any given Boolean function using recombinase-based logic gates. We further develop a methodology leveraging existing electronic design automation (EDA) tools to automate the synthesis of complex recombinase-based genetic circuits with respect to area and delay optimization. Experimental results demonstrate the feasibility of our proposed method.