We measure the imprint of baryon acoustic oscillations (BAOs) in the galaxy clustering pattern at the highest redshift achieved to date, z= 0.6, using the distribution of N= 132 509 emission-line galaxies in the WiggleZ Dark Energy Survey. We quantify BAOs using three statistics: the galaxy correlation function, power spectrum and the band-filtered estimator introduced by Xu et al. The results are mutually consistent, corresponding to a 4.0 per cent measurement of the cosmic distance–redshift relation at z= 0.6 [in terms of the acoustic parameter ‘A(z)’ introduced by Eisenstein et al., we find A(z= 0.6) = 0.452 ± 0.018]. Both BAOs and power spectrum shape information contribute towards these constraints. The statistical significance of the detection of the acoustic peak in the correlation function, relative to a wiggle-free model, is 3.2σ. The ratios of our distance measurements to those obtained using BAOs in the distribution of luminous red galaxies at redshifts z= 0.2 and 0.35 are consistent with a flat Λ cold dark matter model that also provides a good fit to the pattern of observed fluctuations in the cosmic microwave background radiation. The addition of the current WiggleZ data results in a ≈30 per cent improvement in the measurement accuracy of a constant equation of state, w, using BAO data alone. Based solely on geometric BAO distance ratios, accelerating expansion (w < −1/3) is required with a probability of 99.8 per cent, providing a consistency check of conclusions based on supernovae observations. Further improvements in cosmological constraints will result when the WiggleZ survey data set is complete.