Powerful relativistic jets are one of the main ways in which accreting black holes provide kinetic feedback to their surroundings. Jets launched from or redirected by the accretion flow that powers them should be affected by the dynamics of the flow, which in accreting stellar-mass black holes has shown increasing evidence for precession due to frame dragging effects that occur when the black hole spin axis is misaligned with the orbital plane of its companion star. Recently, theoretical simulations have suggested that the jets can exert an additional torque on the accretion flow, although the full interplay between the dynamics of the accretion flow and the launching of the jets is not yet understood. Here we report a rapidly changing jet orientation on a timescale of minutes to hours in the black hole X-ray binary V404 Cygni, detected with very long baseline interferometry during the peak of its 2015 outburst. We show that this can be modelled as Lense-Thirring precession of a vertically-extended slim disk that arises from the super-Eddington accretion rate. Our findings suggest that the dynamics of the precessing inner accretion disk could play a role in either directly launching or redirecting the jets within the inner few hundred gravitational radii. Similar dynamics should be expected in any strongly-accreting black hole whose spin is misaligned with the inflowing gas, both affecting the observational characteristics of the jets, and distributing the black hole feedback more uniformly over the surrounding environment.