High-quality epitaxial thin films of Jeff = 1/2 Mott insulator Sr2IrO4 with increasing in-plane tensile strain have been grown on top of SrTiO3(001) substrates. Increasing the in-plane tensile strain up to ∼0.3% was observed to drop the c/a tetragonality by 1.2%. X-ray absorption spectroscopy detected a strong reduction of the linear dichroism upon increasing in-plane tensile strain towards a reduced anisotropy in the local electronic structure. While the most relaxed thin film shows a consistent dependence with previously reported single crystal bulk measurements, electrical transport reveals a charge gap reduction from 200 meV down to 50 meV for the thinnest and most epitaxy-distorted film. We argue that the reduced tetragonality plays a major role in the change of the electronic structure, which is reflected in the change of the transport properties. Our work opens the possibility for exploiting epitaxial strain as a tool for both structural and functional manipulation of spin-orbit Mott systems.