This paper proposes an Ant Colony Optimization (ACO) approach to solve a variant of the Traveling Salesman Problem called the Random Traveling Salesman Problem (RTSP). In the RTSP, city coordinates are randomly generated rather than using predefined datasets. The ACO model is implemented in MATLAB and tested on randomly generated RTSP datasets ranging from 10 to 200 cities. Results show that the ACO approach finds acceptable solutions and performs well for smaller problem sizes, but performance degrades as the problem size increases. The paper concludes that ACO has potential for solving optimization problems if applied properly.