Understanding and controlling the behaviour of dislocations is crucial for a wide range of applications, from nano-electronics and solar cells to structural engineering alloys. Quantitative X-ray diffraction measurements of the strain fields due to individual dislocations, particularly in the bulk, however, have thus far remained elusive. Here we report the first characterization of a single dislocation in a freestanding GaAs/In0.2Ga0.8As/GaAs membrane by synchrotron X-ray micro-beam Laue diffraction. Our experimental X-ray data agrees closely with textbook anisotropic elasticity solutions for dislocations, providing one of few experimental validations of this fundamental theory. On the basis of the experimental uncertainty in our measurements, we predict the X-ray beam size required for three-dimensional measurements of lattice strains and rotations due to individual dislocations in the material bulk. These findings have important implications for the in situ study of dislocation structure formation, self-organization and evolution in the bulk.