The production cross-sections for W +/- and Z bosons are measured using ATLAS data corresponding to an integrated luminosity of 4.0 pb-1 collected at a centre-ofmass energy v s = 2.76 TeV. The decay channels W and Z. are used, where can be an electron or a muon. The cross-sections are presented for a fiducial region defined by the detector acceptance and are also extrapolated to the full phase space for the total inclusive production cross-section. The combined (average) total inclusive cross-sections for the electron and muon channels are: s tot W+ = 2312 +/- 26 (stat.) +/- 27 (syst.) +/- 72 (lumi.) +/- 30 (extr.) pb, s tot W- = 1399 +/- 21 (stat.) +/- 17 (syst.) +/- 43 (lumi.) +/- 21 (extr.) pb, s tot Z. = 323.4 +/- 9.8 (stat.) +/- 5.0 (syst.) +/- 10.0 (lumi.) +/- 5.5(extr.) pb. Measured ratios and asymmetries constructed using these cross-sections are also presented. These observables benefit from full or partial cancellation of many systematic uncertainties that are correlated between the different measurements.