Pretrained language models can be applied for various downstream tasks but are susceptible to subtle perturbations. Most adversarial defense methods often introduce adversarial training during the fine-tuning phase to enhance empirical robustness. However, the repeated execution of adversarial training hinders training efficiency when transitioning to different tasks. In this paper, we explore the transferability of robustness within subnetworks and leverage this insight to introduce a novel adversarial defense method ORTicket, eliminating the need for separate adversarial training across diverse downstream tasks. Specifically, (i) pruning the full model using the MLM task (the same task employed for BERT pretraining) yields a task-agnostic robust subnetwork(i.e., winning ticket in Lottery Ticket Hypothesis); and (ii) fine-tuning this subnetwork for downstream tasks. Extensive experiments demonstrate that our approach achieves comparable robustness to other defense methods while retaining the efficiency of traditional fine-tuning.This also confirms the significance of selecting MLM task for identifying the transferable robust subnetwork. Furthermore, our method is orthogonal to other adversarial training approaches, indicating the potential for further enhancement of model robustness.