We prove error estimates for the semi-implicit numerical scheme of sphere- constrained high-index saddle dynamics, which serves as a powerful instrument in find- ing saddle points and constructing the solution landscapes of constrained systems on the high-dimensional sphere. Due to the semi-implicit treatment and the novel computational procedure, the orthonormality of numerical solutions at each time step could not be fully employed to simplify the derivations, and the computations of the state variable and direc- tional vectors are coupled with the retraction, the vector transport and the orthonormal- ization procedure, which significantly complicates the analysis. We address these issues to prove error estimates for the proposed semi-implicit scheme and then carry out numerical experiments to substantiate the theoretical findings.