Chain-of-Thought (CoT) reasoning has significantly advanced Large Language Models (LLMs) in solving complex tasks. However, its autoregressive paradigm leads to significant computational overhead, hindering its deployment in latency-sensitive applications. To address this, we propose \textbf{DART} (\textbf{D}istilling \textbf{A}utoregressive \textbf{R}easoning to Silent \textbf{T}hought), a self-distillation framework that enables LLMs to replace autoregressive CoT with non-autoregressive Silent Thought (ST). Specifically, DART introduces two training pathways: the CoT pathway for traditional reasoning and the ST pathway for generating answers directly from a few ST tokens. The ST pathway utilizes a lightweight Reasoning Evolvement Module (REM) to align its hidden states with the CoT pathway, enabling the ST tokens to evolve into informative embeddings. During inference, only the ST pathway is activated, leveraging evolving ST tokens to deliver the answer directly. Extensive experimental results demonstrate that DART offers significant performance gains compared with existing non-autoregressive baselines without extra inference latency, serving as a feasible alternative for efficient reasoning.