Coded aperture X-ray computed tomography is a computational imaging technique capable of reconstructing inner structures of an object from a reduced set of X-ray projection measurements. Coded apertures are placed in front of the X-ray sources from different views and thus significantly reduce the radiation dose. This paper introduces coded aperture X-ray computed tomography for robotic X-ray systems which offer positioning flexibility. While single coded-aperture 3D tomography was recently introduced for standard trajectory CT scanning, it is shown that significant gains in imaging performance can be attained by simple modifications in the CT scanning trajectories enabled by emerging dual robotic CT systems. In particular, the subject is fixed on a plane and the CT system uniformly rotates around the r -axis which is misaligned with the coordinate axes. A single stationary coded aperture is placed on front of the robotic X-ray source above the plane and the corresponding X-ray projections are measured by a two-dimensional detector on the second arm of the robotic system. The compressive measurements with misalignment enable the reconstruction of high-resolution three-dimensional volumetric images from the low-resolution coded projections on the detector at a sub-sampling rate. An efficient algorithm is proposed to generate the rotation matrix with two basic sub-matrices and thus the forward model is formulated. The stationary coded aperture is designed based on the Pearson product-moment correlation coefficient analysis and the direct binary search algorithm is used to obtain the optimized coded aperture. Simulations using simulated datasets show significant gains in reconstruction performance compared to conventional coded aperture CT systems.