We report the use of a surfactant molecule during the epitaxy of graphene on SiC(0001) that leads to the growth in an unconventional orientation, namely R0° rotation with respect to the SiC lattice. It yields a very high-quality single-layer graphene with a uniform orientation with respect to the substrate, on the wafer scale. We find an increased quality and homogeneity compared to the approach based on the use of a preoriented template to induce the unconventional orientation. Using spot profile analysis low-energy electron diffraction, angle-resolved photoelectron spectroscopy, and the normal incidence x-ray standing wave technique, we assess the crystalline quality and coverage of the graphene layer. Combined with the presence of a covalently bound graphene layer in the conventional orientation underneath, our surfactant-mediated growth offers an ideal platform to prepare epitaxial twisted bilayer graphene via intercalation.