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-of-mass energy s=2.76 TeV. The decay channels W→ ℓν and Z→ ℓℓ are used, where ℓ 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: σW+→ℓνtot=2312±26(stat.)±27(syst.)±72(lumi.)±30(extr.)pb,σW-→ℓνtot=1399±21(stat.)±17(syst.)±43(lumi.)±21(extr.)pb,σZ→ℓℓtot=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.