We present the results of a search for pair production of scalar top quarks (t˜1) in an R-parity violating supersymmetry scenario in 106   pb−1 of pp¯ collisions at s√=1.8  TeV collected by the Collider Detector at Fermilab. In this mode each t˜1 decays into a τ lepton and a b quark. We search for events with two τ's, one decaying leptonically (e or μ) and one decaying hadronically, and two jets. No candidate events pass our final selection criteria. We set a 95% confidence level lower limit on the t˜1 mass at 122  GeV/c2 for Br(t˜1→τb)=1.