New rapid diagnostic tests (RDTs) for screening human African trypanosomiasis (HAT) have been introduced as alternatives to the card agglutination test for trypanosomiasis (CATT). One brand of RDT, the SD BIOLINE HAT RDT has been shown to have lower specificity but higher sensitivity than CATT, so to make a rational choice between screening strategies, a cost-effectiveness analysis is a key element. In this paper we estimate the relative cost-effectiveness of CATT and the RDT when implemented in the Democratic Republic of the Congo (DRC). Data on the epidemiological parameters and costs were collected as part of a larger study. These data were used to model three different diagnostic algorithms in mobile teams and fixed health facilities, and the relative cost-effectiveness was measured as the average cost per case diagnosed. In both fixed facilities and mobile teams, screening of participants using the SD BIOLINE HAT RDT followed by parasitological confirmation had a lower cost-effectiveness ratio than in algorithms using CATT. Algorithms using the RDT were cheaper by 112.54 (33.2%) and 88.54 (32.92%) US dollars per case diagnosed in mobile teams and fixed health facilities respectively, when compared with algorithms using CATT. Sensitivity analysis demonstrated that these conclusions were robust to a number of assumptions, and that the results can be scaled to smaller or larger facilities, and a range of prevalences. The RDT was the most cost-effective screening test in all realistic scenarios and detected more cases than CATT. Thus, on this basis, the SD BIOLINE HAT RDT could be considered as the most cost-effective option for use in routine screening for HAT in the DRC.