Light beams carrying orbital angular momentum (OAM) have led to stunning applications in various fields from quantum information to microscopy. We examine OAM from the recently observed high-harmonic generation (HHG) in semiconductor crystals. HHG from solids could be a valuable approach for integrated high-flux short-wavelength coherent light sources. First, we verify the transfer and conservation of the OAM in the strong-field regime of interaction from the generation laser to the harmonics. Secondly, we create OAM beams by etching a spiral zone structure directly at the surface of a zinc oxide crystal. Such diffractive optics act on the generated harmonics and produces focused optical vortices with sub-micrometric size.