While deep learning has achieved significant success in various domains, its application to logic circuit design has been limited due to complex constraints and strict feasibility requirement. However, a recent generative deep neural model, "Circuit Transformer", has shown promise in this area by enabling equivalence-preserving circuit transformation on a small scale. In this paper, we introduce a logic synthesis rewriting operator based on the Circuit Transformer model, named "ctrw" (Circuit Transformer Rewriting), which incorporates the following techniques: (1) a two-stage training scheme for the Circuit Transformer tailored for logic synthesis, with iterative improvement of optimality through self-improvement training; (2) integration of the Circuit Transformer with state-of-the-art rewriting techniques to address scalability issues, allowing for guided DAG-aware rewriting. Experimental results on the IWLS 2023 contest benchmark demonstrate the effectiveness of our proposed rewriting methods.