We show that in the first order gravity theory coupled to axions, there exist new kind of instanton configurations (solutions of Euclidean equations of motion) whose instanton number can be interpreted as the torsional Nieh-Yan topological index. These torsional pseudoparticles turn out to be the Giddings-Strominger wormholes. Importantly, these instantons are shown to induce tunneling between degenerate topological vacua in gravity theory, leading to a rich vacuum structure exactly similar to the famous theta vacuum of gauge theories. This nonperturbative quantum vacuum is characterised by a topological vacuum angle, which can be identified with the Barbero-Immirzi parameter. We conclude with a discussion on how this nonperturbative vacuum structure in quantum gravity, hitherto unnoticed, could have important implications in the context of cosmology and various parity violating phenomena in particle physics. In particular, based on this framework we propose a solution to the cosmological constant problem.