Despite their importance, very few RR Lyrae (RRL) stars have been known to reside in binary systems. We report on a search for binary RRL in the OGLE-III Galactic bulge data. Our approach consists in the search for evidence of the light-travel time effect in so-called observed minus calculated (O-C) diagrams. Analysis of 1952 well-observed fundamental-mode RRL in the OGLE-III data revealed an initial sample of 29 candidates. We used the recently released OGLE-IV data to extend the baselines up to 17 yr, leading to a final sample of 12 firm binary candidates. We provide O-C diagrams and binary parameters for this final sample, and also discuss the properties of eight additional candidate binaries whose parameters cannot be firmly determined at present. We also estimate that a parts per thousand(3) 4 per cent of the RRL reside in binary systems.