Magnetic resonance imaging (MRI) is a vital clinical diagnostic tool, yet its application is limited by prolonged scan times. Accelerating MRI reconstruction addresses this issue by reconstructing high-fidelity MR images from undersampled k-space measurements. In recent years, deep learning-based methods have demonstrated remarkable progress. However, most methods rely on supervised learning, which requires large amounts of fully-sampled training data that are difficult to obtain. This paper proposes a novel zero-shot self-supervised reconstruction method named UnrollINR, which enables scan-specific MRI reconstruction without external training data. UnrollINR adopts a physics-guided unrolled reconstruction architecture and introduces implicit neural representation (INR) as a regularization prior to effectively constrain the solution space. This method overcomes the local bias limitation of CNNs in traditional deep unrolled methods and avoids the instability associated with relying solely on INR's implicit regularization in highly ill-posed scenarios. Consequently, UnrollINR significantly improves MRI reconstruction performance under high acceleration rates. Experimental results show that even at a high acceleration rate of 10, UnrollINR achieves superior reconstruction performance compared to supervised and self-supervised learning methods, validating its effectiveness and superiority.