The article presents the results of research concerning the analysis of the possibility of the innovative application of the LineScan non-contact laser measuring probe controlled by the ACCURA II coordinate measuring machine in the field of measurements of a selected cutting tool. In the study, the angle of a round cutting insert was measured. The influence of the selected elements of a measurement strategy i.e., the scanning speed v, the resolution k, and the number of measurement paths w on the repeatability of measurements and the value of the insert’s angle was determined. In both cases, the number of paths had the greatest impact. The best repeatability was obtained for the smallest distance between points (k = 0.1 mm) and the largest number of paths (w =10). For those measurement strategies, which differed in the scanning speed (1 and 3 mm/s), the detailed GR&R analyses were carried out by using the ANOVA and EMP methods. For strategies with the scanning speeds of 1 and 3 mm/s, the variance of the measuring system was 0.9% and 0.5% of the total variance, respectively. However, these differences in repeatability were not statistically significant. It has been shown that the selected methodologies of measurements and measurement data processing ensure good measurement repeatability of the selected geometrical feature of a cutting tool.