  We carry out the renormalization and the Symanzik O(a)-improvement programme
for the static vector current in quenched lattice QCD. The scale independent
ratio of the renormalization constants of the static vector and axial currents
is obtained non-perturbatively from an axial Ward identity with Wilson-type
light quarks and various lattice discretizations of the static action. The
improvement coefficients cVstat and bVstat are obtained up to O(g_0^4)-terms by
enforcing improvement conditions respectively on the axial Ward identity and a
three-point correlator of the static vector current. A comparison between the
non-perturbative estimates and the corresponding one-loop results shows a
non-negligible effect of the O(g_0^4)-terms on the improvement coefficients but
a good accuracy of the perturbative description of the ratio of the
renormalization constants.
