This article presents a motion compensation procedure that significantly improves the accuracy of synthetic aperture tensor velocity estimates for row-column arrays. The proposed motion compensation scheme reduces motion effects by moving the image coordinates with the velocity field during summation of low-resolution volumes. The velocity field is estimated using a transverse oscillation cross-correlation estimator, and each image coordinate's local tensor velocity is determined by upsampling the field using spline interpolation. The motion compensation procedure is validated using Field II simulations and flow measurements acquired using a 3-MHz row-column addressed probe and the research scanner SARUS. For a peak velocity of 25 cm/s, a pulse repetition frequency of 2 kHz, and a beam-to-flow angle of 60°, the proposed motion compensation procedure was able to reduce the relative bias from -27.0% to -9.4% and the standard deviation from 8.6% to 8.1%. In simulations performed with a pulse repetition frequency of 10 kHz, the proposed method reduces the bias in all cases with beam-to-flow angles of 60° and 75° and peak velocities between 10 and 150 cm/s.