Adversarial robustness and privacy of deep learning (DL) models are two widely studied topics in AI security. Adversarial training (AT) is an effective approach to improve the robustness of DL models against adversarial attacks. However, while models with AT demonstrate enhanced robustness, they become more susceptible to membership inference attacks (MIAs), thus increasing the risk of privacy leakage. This indicates a negative trade-off between adversarial robustness and privacy in general deep learning models. Visual prompting is a novel model reprogramming (MR) technique used for fine-tuning pre-trained models, achieving good performance in vision tasks, especially when combined with the label mapping technique. However, the performance of label-mapping-based visual prompting (LM-VP) under adversarial attacks and MIAs lacks evaluation. In this work, we regard the MR of LM-VP as a unified entity, referred to as the LM-VP model, and take a step toward jointly evaluating the adversarial robustness and privacy of LM-VP models. Experimental results show that the choice of pre-trained models significantly affects the white-box adversarial robustness of LM-VP, and standard AT even substantially degrades its performance. In contrast, transfer AT-trained LM-VP achieves a good trade-off between transferred adversarial robustness and privacy, a finding that has been consistently validated across various pre-trained models. Code is available at https://github.com/TrustAI/TARP-VP.