Instruction tuning has underscored the significant potential of large language models (LLMs) in producing more human controllable and effective outputs in various domains. In this work, we focus on the data selection problem for task-specific instruction tuning of LLMs. Prevailing methods primarily rely on the crafted similarity metrics to select training data that aligns with the test data distribution. The goal is to minimize instruction tuning loss on the test data, ultimately improving performance on the target task. However, it has been widely observed that instruction tuning loss (i.e., cross-entropy loss for next token prediction) in LLMs often fails to exhibit a monotonic relationship with actual task performance. This misalignment undermines the effectiveness of current data selection methods for task-specific instruction tuning. To address this issue, we introduce ROSE, a novel Reward-Oriented inStruction data sElection method which leverages pairwise preference loss as a reward signal to optimize data selection for task-specific instruction tuning. Specifically, ROSE adapts an influence formulation to approximate the influence of training data points relative to a few-shot preference validation set to select the most task-related training data points. Experimental results show that by selecting just 5\% of the training data using ROSE, our approach can achieve competitive results compared to fine-tuning with the full training dataset, and it surpasses other state-of-the-art data selection methods for task-specific instruction tuning. Our qualitative analysis further confirms the robust generalizability of our method across multiple benchmark datasets and diverse model architectures.