This paper presented the capability of Sine Cosine Algorithm (SCA) in handling curve representation problems. SCA is used to capture the outlines of Arabic fonts by using cubic Bézier curve. There are several pre-processing steps involved before the curve fitting process, which include boundary extraction, corner detection and chord length parameterization. SCA is then used to optimize the middle points of the cubic Bézier curve. The final results will be visually and numerically presented. The numerical errors are found by calculating sum square errors (SSE). SSE will be the objective function for this optimization problem. SCA will search for the best middle control points by minimizing SSE. SSE is calculated by comparing the reconstructed curve with the original curve. The proposed method is then compared with the least square method (LSM). The results have shown that SCA is better than LSM.