We report on the experimental realization of a Kapitza trap for ultracold atoms. Using time-periodic attractive and repulsive Gaussian potentials, we create an effective trap for ultracold neutral atoms in a regime where the time average of the potential is equal to zero. We analyze the role of experimental imperfections, the stability of the trapped atomic cloud, and the magnitude of the effective potential. We find good agreement with the high-frequency expansion of the underlying system dynamics. Our experimental approach opens up new possibilities to study Floquet systems of neutral atoms.