Vision Transformers (ViTs) have demonstrated the state-of-the-art performance in various vision-related tasks. The success of ViTs motivates adversaries to perform backdoor attacks on ViTs. Although the vulnerability of traditional CNNs to backdoor attacks is well-known, backdoor attacks on ViTs are seldom-studied. Compared to CNNs capturing pixel-wise local features by convolutions, ViTs extract global context information through patches and attentions. Naïvely transplanting CNN-specific backdoor attacks to ViTs yields only a low clean data accuracy and a low attack success rate. In this paper, we propose a stealth and practical ViT-specific backdoor attack TrojViT. Rather than an area-wise trigger used by CNN-specific backdoor attacks, TrojViT generates a patch-wise trigger designed to build a Trojan composed of some vulnerable bits on the parameters of a ViT stored in DRAM memory through patch salience ranking and attention-target loss. TrojViT further uses parameter distillation to reduce the bit number of the Trojan. Once the attacker inserts the Trojan into the ViT model by flipping the vulnerable bits, the ViT model still produces normal inference accuracy with benign inputs. But when the attacker embeds a trigger into an input, the ViT model is forced to classify the input to a predefined target class. We show that flipping only few vulnerable bits identified by TrojViT on a ViT model using the well-known RowHammer can transform the model into a backdoored one. We perform extensive experiments of multiple datasets on various ViT models. TrojViT can classify 99.64% of test images to a target class by flipping 345 bits on a ViT for ImageNet.