Kolmogorov-Arnold Networks (KANs) have emerged as a powerful framework for modeling complex functions with minimal architecture, which can be a novel solution for Artificial Intelligence (AI) modeling. However, implementing KANs in hardware presents significant challenges due to their reliance on nonlinear functions. In this paper, we introduce the Stochastic Computing-based Kolmogorov-Arnold Network (SCKAN) Accelerator, the first known accelerator for KANs that leverages stochastic computing to effectively address these challenges. We propose a Segmented Multi-Dimensional Multi-Driving Finite State Machine (SMM-FSM) to efficiently approximate a broad range of nonlinear functions, enabling flexible and accurate network tuning. Our accuracy analysis demonstrates the feasibility of implementing KANs using stochastic computing. The SCKAN architecture integrates SMM-FSMs with crossbar networks, efficiently managing interconnections within the KAN. Through evaluations, we show that SCKAN achieves area reductions of 1.33 to 5.17× and power savings of 1.37 to 2.65× compared to traditional methods such as Look-Up Tables (LUTs), Taylor series expansion, and the Coordinate Rotation Digital Computer (CORDIC) algorithm. It maintains high accuracy in function-fitting tasks and minimal accuracy loss in classification tasks. SCKAN thus offers an effective solution for deploying KANs in resource-constrained environments, marking a significant advancement in the hardware implementation of nonlinear models.