This letter presents a search for singly produced vector-like quarks, Q, coupling to light quarks, q. The search is sensitive to both charged current (CC) and neutral current (NC) processes, p p --> Q q --> W q q' and p p --> Q q --> Z q q' with a leptonic decay of the vector gauge boson. In 1.04/fb of data taken in 2011 by the ATLAS experiment at a center-of-mass energy sqrt(s) = 7 TeV, no evidence of such heavy vector-like quarks is observed above the expected Standard Model background. Limits on the heavy vector-like quark production cross section times branching ratio as a function of mass m_Q are obtained. For a coupling kappa_(qQ) = v/m_Q, where v is the Higgs vacuum expectation value, 95% C.L. lower limits on the mass of a vector-like quark are set at 900 GeV and 760 GeV from CC and NC processes, respectively. Show Partial Abstract