Herein, a radius-constrained iterative reweighted least squares circle fitting (RC-IRLSCF) method is proposed to address the problems of very small angle of the circle corresponding to arc characteristic data collected by the line laser displacement sensor, noise and outliers in the characteristic points, and others, which seriously affect the positioning accuracy of the circle center. To overcome the influence of noise and outliers on detection accuracy during the detection of existing arc features, a circle-fitting target optimization model based on radius constraints and robust loss function is constructed using iterative reweighting and Levenberg-Marquardt algorithm to further optimize the solution and achieve accurate fitting and positioning of arc features. The detection experiment of the service wheel tread surface shows the use of line laser in detecting contour arc characteristics. Moreover, the proposed method can realize accurate fitting and positioning of the arc under the condition that light scattering and local deformation produce adjacent outliers, with a certain degree of robustness and noise resistance.