This paper describes a semi-parametric Bayesian approach for estimating receiver operating characteristic (ROC) curves based on mixtures of Dirichlet process priors (MDP). We address difficulties in modelling the underlying distribution of screening scores due to non-normality that may lead to incorrect choices of diagnostic cut-offs and unreliable estimates of prevalence of the disease. MDP is a robust tool for modelling non-standard diagnostic distributions associated with imperfect classification of an underlying diseased population, for example, when a diagnostic test is not a gold standard. For posterior computations, we propose an efficient Gibbs sampling framework based on a finite-dimensional approximation to MDP. We show, using both simulated and real data sets, that MDP modelling for ROC curve estimation closely parallels the frequentist kernel density estimation (KDE) approach.