The static quadrupole polarizabilities for hydrogen-like ions from Z = 1 to Z = 100 in the 1S 1/2 ground state are calculated to high precision by solving the Dirac equation using the B-spline Galerkin method. The results are consistent with the expression of Kaneko [J. Phys. B 10 (1977) 3347] at low Z. The quadrupole oscillator strength sum ? nf (2) gn is computed to be zero to a very high degree of precision.