Mass flow inequality in the initial stage of tube processing can lead to eccentricity and micro- and nano-structural changes that affect residual stress and texture development. In this study, the macro- and micro-texture development of copper tubes drawn with a tilted die was investigated using three methods: synchrotron, neutron diffraction, and electron backscatter diffraction, in the positions of maximum and minimum wall thickness of the tubes. Understanding how a tilted die can affect the texture development in copper tubes is the main aim of this study. The micro-texture results of EBSD examinations showed the same behavior at the maximum and minimum sides of the as-received tube, as observed using the synchrotron diffraction method as well as macro-texture measurements. The cube texture component was found to be the predominant orientation in the as-received tube. However, it almost disappeared after drawing with −5° tilting. By contrast, the Cu texture component increased significantly. Before drawing, the cube component varied strongly across the wall thickness. After drawing, however, there was no noticeable texture gradient across the wall thickness. The analyses showed that tilting is not creating an inhomogeneous texture development over the circumference.