Controlled fusion energy is deemed pivotal for the advancement of human civilization. In this study, we introduce $\textbf{Fusion-LLM}$, a novel integration of Large Language Models (LLMs) with classical reservoir computing paradigms tailored to address challenges in Inertial Confinement Fusion ($\texttt{ICF}$). Our approach offers several key contributions: Firstly, we propose the $\textit{LLM-anchored Reservoir}$, augmented with a fusion-specific prompt, enabling accurate forecasting of hot electron dynamics during implosion. Secondly, we develop $\textit{Signal-Digesting Channels}$ to temporally and spatially describe the laser intensity across time, capturing the unique characteristics of $\texttt{ICF}$ inputs. Lastly, we design the $\textit{Confidence Scanner}$ to quantify the confidence level in forecasting, providing valuable insights for domain experts to design the $\texttt{ICF}$ process. Extensive experiments demonstrate the superior performance of our method, achieving 1.90 CAE, 0.14 $\texttt{top-1}$ MAE, and 0.11 $\texttt{top-5}$ MAE in predicting Hard X-ray ($\texttt{HXR}$) energies of $\texttt{ICF}$ tasks, which presents state-of-the-art comparisons against concurrent best systems. Additionally, we present $\textbf{Fusion4AI}$, the first $\texttt{ICF}$ benchmark based on physical experiments, aimed at fostering novel ideas in plasma physics research and enhancing the utility of LLMs in scientific exploration. Overall, our work strives to forge an innovative synergy between AI and plasma science for advancing fusion energy.