Instruction-tuned models are trained on crowdsourcing datasets with task instructions to achieve superior performance. However, in this work we raise security concerns about this training paradigm. Our studies demonstrate that an attacker can inject backdoors by issuing very few malicious instructions among thousands of gathered data and control model behavior through data poisoning, without even the need of modifying data instances or labels themselves. Through such instruction attacks, the attacker can achieve over 90% attack success rate across four commonly used NLP datasets, and cause persistent backdoors that are easily transferred to 15 diverse datasets zero-shot. In this way, the attacker can directly apply poisoned instructions designed for one dataset on many other datasets. Moreover, the poisoned model cannot be cured by continual learning. Lastly, instruction attacks show resistance to existing inference-time defense. These findings highlight the need for more robust defenses against data poisoning attacks in instructiontuning models and underscore the importance of ensuring data quality in instruction crowdsourcing.