The use of optical forces to manipulate small objects is well known. Applications include the manipulation of living cells by optical tweezers and optical cooling in atomic physics. The miniaturization of optical systems (to the micro and nanoscale) has resulted in very compliant systems with masses of the order of nanograms, rendering them susceptible to optical forces. Optical forces have been exploited to demonstrate chaotic quivering of microcavities, optical cooling of mechanical modes, actuation of a tapered-fibre waveguide and excitation of the mechanical modes of silicon nano-beams. Despite recent progress in this field, it is challenging to manipulate the optical response of photonic structures using optical forces; this is because of the large forces that are required to induce appreciable changes in the geometry of the structure. Here we implement a resonant structure whose optical response can be efficiently statically controlled using relatively weak attractive and repulsive optical forces. We demonstrate a static mechanical deformation of up to 20 nanometres in a silicon nitride structure, using three milliwatts of continuous optical power. Because of the sensitivity of the optical response to this deformation, such optically induced static displacement introduces resonance shifts spanning 80 times the intrinsic resonance linewidth.