Thin ferroelectric barium strontium titanate (BST) layers of high structure quality have been grown for the first time directly on semi-insulating silicon carbide substrates by RF magnetron sputtering of a ceramic target. The structural and microwave properties of the films were substantially improved by an intermediate annealing of the layers during the growing process. Prepared under this approach, BST films have a well-formed crystal structure, which has a positive effect on their electrical properties, specifically on nonlinearity and dielectric losses. Planar capacitors based on these BST films demonstrate the best combination of high tunability and low losses for BST/SiC structures at microwaves.