During non-landing measurements of a theodolite, the accuracy of the goniometric readings can be compromised by wobble errors induced by various factors such as wind loads, theodolite driving torque, and the stiffness of the supporting structure. To achieve high-precision non-landing measurements, it is essential to accurately determine and correct the platform wobble errors affecting the azimuth and pitch pointing angles. In this paper, a non-contact optical measurement method is proposed for quantifying platform wobble errors. The method establishes an auto-alignment optical path between an autocollimator and a reflector in the measuring device. By detecting the deviation angle of the CCD image point as the optical path changes, precise measurements of the platform wobble errors can be obtained. Experimental results demonstrate that the measuring device can achieve an auto-alignment optical path within 5 minutes, significantly improving measurement efficiency. Furthermore, after measuring the platform wobble error and applying data correction, the average error in the azimuth pointing angle is reduced from 31.5″ to 9.8″, and the average error in the pitch pointing angle is reduced from 21″ to 9.2″. These results highlight the substantial correction effect achieved by the proposed method.