Medical image segmentation is critical for accurate diagnostics and treatment planning, but remains challenging due to complex anatomical structures and limited annotated training data. CNN-based segmentation methods excel at local feature extraction, but struggle with modeling long-range dependencies. Transformers, on the other hand, capture global context more effectively, but are inherently data-hungry and computationally expensive. In this work, we introduce UKAST, a U-Net like architecture that integrates rational-function based Kolmogorov-Arnold Networks (KANs) into Swin Transformer encoders. By leveraging rational base functions and Group Rational KANs (GR-KANs) from the Kolmogorov-Arnold Transformer (KAT), our architecture addresses the inefficiencies of vanilla spline-based KANs, yielding a more expressive and data-efficient framework with reduced FLOPs and only a very small increase in parameter count compared to SwinUNETR. UKAST achieves state-of-the-art performance on four diverse 2D and 3D medical image segmentation benchmarks, consistently surpassing both CNN- and Transformer-based baselines. Notably, it attains superior accuracy in data-scarce settings, alleviating the data-hungry limitations of standard Vision Transformers. These results show the potential of KAN-enhanced Transformers to advance data-efficient medical image segmentation. Code is available at: https://github.com/nsapkota417/UKAST