We present a detailed analysis of new ALMA observations of the disk around the T-Tauri star HD 143006, which at 46 mas (7.6 au) resolution reveal new substructures in the 1.25 mm continuum emission. The disk resolves into a series of concentric rings and gaps together with a bright arc exterior to the rings that resembles hydrodynamics simulations of a vortex, and a bridge-like feature connecting the two innermost rings. Although our $^{12}$CO observations at similar spatial resolution do not show obvious substructure, they reveal an inner disk depleted of CO emission. From the continuum emission and the CO velocity field we find that the innermost ring has a higher inclination than the outermost rings and the arc. This is evidence for either a small ($sim8^{circ}$) or moderate ($sim41^{circ}$) misalignment between the inner and outer disk, depending on the specific orientation of the near/far sides of the inner/outer disk. We compare the observed substructures in the ALMA observations with recent scattered light data from VLT/SPHERE of this object. In particular, the location of narrow shadow lanes in the SPHERE image combined with pressure scale height estimates, favor a large misalignment of about $41^{circ}$. We discuss our findings in the context of a dust-trapping vortex, planet-carved gaps, and a misaligned inner disk due to the presence of an inclined companion to HD 143006.