Steering Vector (SV) is a powerful technique for controlling Large Language Models (LLMs) by manipulating their activations without altering model weights. However, when constructed from sensitive data, SV poses significant privacy risks, as it may leak private information. Existing differential privacy (DP) techniques for constructing SV cannot be directly applied to training-based SV construction paradigms, which offer higher task performance. In this work, we present PrivSV, a general privacy-preserving approach for constructing SV with DP guarantees, compatible with arbitrary SV construction paradigms while maintaining high utility. In PrivSV, we propose three novel methods: a Layer-wise Noise-Resilient Reduction (LNR²) method to reduce the injected noise in high-dimensional SV; a Directional Prior Compensation (DPC) method to recover utility degraded by noise perturbation; and a Privacy-Aware Optimal Parameter Determination (POPD) method to adaptively maximize the performance of the final compensated SV. Extensive experiments on open-source LLMs of different families (i.e., LlaMa, Qwen, Mistral and Gemma) demonstrate that PrivSV outperforms several existing techniques across various privacy budgets.