Explicit channel state information (CSI) feedback in IEEE~802.11 conveys \emph{transmit beamforming directions} by reporting quantized Givens rotation and phase angles that parametrize the right-singular subspace of the channel matrix. Because these angles encode fine-grained spatial signatures of the propagation environment, recent work have shown that plaintext CSI feedback can inadvertently reveal user activity, identity, and location to passive eavesdroppers. In this work, we introduce a standards-compatible \emph{differentially private (DP) quantization mechanism} that replaces deterministic angular quantization with an $\varepsilon$-DP stochastic quantizer applied directly to the Givens parameters of the transmit beamforming matrix. The mechanism preserves the 802.11 feedback structure, admits closed-form sensitivity bounds for the angular representation, and enables principled privacy calibration. Numerical simulations demonstrate strong privacy guarantees with minimal degradation in beamforming performance.