Piezoelectric stretching of optical fiber is a technique that enables the creation of optical delays of a few picoseconds; this is useful in a variety of applications in interferometry or optical cavities. Most commercial fiber stretchers involve lengths of fiber of a few tens of meters. Using a 120-mm-long optical micro-nanofiber, we can create a compact optical delay line that achieves tunable delays of up to 19 ps at telecommunication wavelengths. The high elasticity of silica and the micron-scale diameter allow this significant optical delay to be achieved with low tensile force while keeping the overall length short. We successfully report both static and dynamic operation of this novel, to the best of our knowledge, device. It could find application in interferometry and laser cavity stabilization, where short optical paths and strong resistance to the environment would be required.