In this paper, the effects of calcium carbonate powder on the properties of self-consolidating concrete (SCC) incorporated with untreated rice husk ash (RHA) and calcium carbonate powder (CC) are presented. CC was utilized as an ordinary Portland cement (OPC) substitute at percentage replacements of 20% and 40% by weight, and RHA was used as a fine aggregate replacement material at a percentage replacement of 20% by weight. The SCC mixtures were designed with a controlled slump flow of 725 ± 25 mm. The properties in the fresh and hardened states of the blends of OPC and CC were investigated using the slump flow time, V-funnel flow time, flow diameter from the J-ring test, compressive strength, and resistance to sulfuric acid attack. The results showed that the use of CC can reduce the water content of the powder materials (OPC + CC). Remarkably, the resulting concretes maintained their slump flow and could flow through a V-shaped box and the obstacles used to assess the J-ring test, thus satisfying the criterion declared by European Federation of Producers and Applicators of Specialist Products for Structures (EFNARC). Moreover, the highest compressive strength was achieved in the SCC mixture with 20% CC1 (Dv, 50 = 3.95 μm). Compared with SCC without RHA, the addition of RHA requires an increased ratio of water/powder (w/p) materials (OPC + CC). Furthermore, in the case of concrete without RHA, the SCC containing CC exhibited a lower weight loss after sulfuric acid (H2SO4) attack than the control SCC.