The production of a quartz glass grit comprises the granulation of pyrogenetically produced silicic acid, and the formation of a SiO2 granulate and the vitrification of the SiO2 granulate using a treatment gas, which contains at least 30% by volume of helium and/or hydrogen. Said process is time consuming and cost intensive. In order to provide a method which makes it possible, starting from a porous SiO2 granulate, to manufacture, in a cost effective manner, a dense, synthetic quartz glass grit, which is suitable for melting bubble-free components made of quartz glass, according to the invention the vitrification of the SiO2 granulate occurs in a rotary kiln having a mullite-containing ceramic rotary kiln, for the manufacture of which a starting powder, which contains a molar proportion of at least 45% SiO2 and Al2O3 is applied by means of a thermal powder spraying method, forming a mullite-containing layer on a mold core, and the mold core is subsequently removed, and wherein the ceramic rotary kiln is flooded with a treatment gas or rinsed with a treatment gas, and wherein the ceramic rotary kiln is flooded with a treatment gas or rinsed with a treatment gas, which contains at least 30% by volume of helium and/or hydrogen.