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In this paper, we propose a novel application of Redundant Residue Number System (RRNS) codes to Space-Time Block Codes (STBCs) design. Based on the so-called "Direct Mapping" and "Indirect Mapping" schemes, the link between residues and complex signal constellations is optimized. We derive upper bounds on the codeword error probability of RRNS-STBC and characterize its achievable diversity gain assuming maximum likelihood decoding (MLD). The knowledge of apriori probabilities of residues is utilized to implement a probability based Distance-Aware Direct Mapping scheme. Using simulation results, we demonstrate that the Distance-Aware Direct Mapping scheme provides performance gain, relative to a traditional direct mapping scheme, that increases with decreasing code rate. [ABSTRACT FROM AUTHOR]