The trend for vehicle automation in the recent decades caused a significant growth of researches in autonomous navigation of robotized cars, obstacle avoidance, and dynamic path planning. This paper presents an algorithm for autonomous perpendicular parking of an Avrora Unior car-like mobile robot. The parking process includes finding a suitable parking space and a perpendicular park maneuver. The proposed solution uses point clustering to accurately determine a parking space. A free space is qualified as a parking plot automatically when the threshold value of the distance between clusters is reached. The parking maneuver involves aligning the robot to the parking slot and moving along an arc-shaped trajectory. The algorithm uses only LiDAR and wheel encoder data to determine the robot’s location relative to parking spaces. The quality of the robot’s parking is estimated by the distance to the boundaries of the parking space. The reliability of the algorithm was successfully validated in Gazebo simulation and in real-world experiments.