This paper investigates a practical partially-connected hybrid beamforming transmitter for integrated sensing and communication (ISAC) with distortion from nonlinear power amplification. For this ISAC system, we formulate a communication rate and sensing mutual information maximization problem driven by our distortion-aware hybrid beamforming design. To address this non-convex problem, we first solve for a fully digital beamforming matrix by alternatively solving three sub-problems using manifold optimization (MO) and our derived closed-form solutions. The analog and digital beamforming matrices are then obtained through a decomposition algorithm. Numerical results demonstrate that the proposed algorithm can improve overall ISAC performance compared to traditional beamforming methods.