This study aims to compare the torque values for various lengths of the titanium-based orthodontic anchor screw (OAS), different anchorage methods and varying artificial bone densities after predrilling. Furthermore, the effects of these parameters on bone stability are evaluated. A total of 144 OASs were prepared with a diameter of 1.6 mm and heights of 6, 8 and 10 mm. Artificial bones were selected according to their density, corresponding to Grades 50, 40 and 30. Torque values for the automatic device and manual anchorage methods exhibited a statistically significant difference for the same-sized OAS, according to the bone density of the artificial bones (p < 0.05). However, when insertion torque was at the maximum rotations, there was no significant difference in the torque values for the Grade 30 artificial bone (p > 0.05). When the torque values of both anchorage methods were statistically compared with the mean difference for each group, the results of the manual anchorage method were significantly higher than those of the automatic device anchorage method (p < 0.05). A statistically significant difference was observed in the bone stability resulting from different OAS anchorage methods and artificial bone lengths. These findings suggest that the automatic anchorage method should be used when fixing the OAS.