This paper presents a search for the t-channel exchange of an R-parity violating scalar top quark (t) in the e±μ∓ continuum using 2.1 fb−1 of data collected by the ATLAS detector in √s = 7 TeV pp collisions at the Large Hadron Collider. Data are found to be consistent with the expectation from the Standard Model backgrounds. Limits on R-parity-violating couplings at 95 % C.L. are calculated as a function of the scalar top mass (mt). The upper limits on the production cross section for pp→eμX, through the t-channel exchange of a scalar top quark, ranges from 170 fb for mt = 95 GeV to 30 fb for mt = 1000 GeV.