DNA origami enables fabrication of precise nanostructures by programming the self-assembly of DNA. While this approach has been used to make a variety of complex 2D and 3D objects, the mechanical functionality of these structures is limited due to their rigid nature. We explore the fabrication of deformable, or compliant, objects to establish a framework for mechanically functional nanostructures. This compliant design approach is used in macroscopic engineering to make devices including sensors, actuators, and robots. We build compliant nanostructures by utilizing the entropic elasticity of single-stranded DNA (ssDNA) to locally bend bundles of double-stranded DNA into bent geometries whose curvature and mechanical properties can be tuned by controlling the length of ssDNA strands. We demonstrate an ability to achieve a wide range of geometries by adjusting a few strands in the nanostructure design. We further developed a mechanical model to predict both geometry and mechanical properties of our compliant nanostructures that agrees well with experiments. Our results provide a basis for the design of mechanically functional DNA origami devices and materials.