At the electron accelerator ELSA a linearly polarised tagged photon beam is produced by coherent bremsstrahlung off a diamond crystal. Orientation and energy range of the linear polarisation can be deliberately chosen by accurate positioning of the crystal with a goniometer. The degree of polarisation is determined by the form of the scattered electron spectrum. Good agreement between experiment and expectations on basis of the experimental conditions is obtained. Polarisation degrees of P = 40% are typically achieved at half of the primary electron energy. The determination of P is confirmed by measuring the beam asymmetry, Sigma, in pi^0 photoproduction and a comparison of the results to independent measurements using laser backscattering.