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This study examines the effects of different intermediate annealing times during multi-pass cold-torsion tests on the microstructure in alloys of aluminum, magnesium, silicon, and copper (Al–Mg–Si–Cu). The mean flow stress, when the intermediate annealing time is shorter, increases until sufficient internal strain accumulates and then decreases rapidly. In contrast, the mean flow stress decreases continuously when the IA time is longer. X-ray line profile analysis revealed a rapid decrease in mean flow stress because of the high stored internal energy represented by the dislocation density. In addition, a short annealing time allows the B component to form in the initial stage of multi-pass torsion, and a random texture distribution occurs as the multi-pass torsion stage progresses. In contrast, a long annealing time can dissipate the texture distribution in a low-pass stage (low strain) and decreases the overall deformation resistance, despite the much stronger texture intensity in a high-strain area. Finally, the B texture component is consumed by the A component in the initial stages of the multi-pass cold torsion test. This is attributed to the different orientation relationships of the shear plane in the A and B components, which caused deviations in dislocation density.