Palm oil clinker (POC) aggregates is a viable alternative to the naturally occurring sand and gravel in the manufacturing of concrete. The usage of POC aggregates assists in the reduction of solid waste and preserves the consumption of natural resources. Although researchers investigated the mechanical response of POC-containing concrete, limited research is available for its torsional behavior. In general, the torsional strength depends on the tensile strength of concrete. This research investigates the compressive, tensile, and torsional response of concrete with various ratios of POC-aggregates. Five batches of concrete were casted with POC-aggregate replacing granite at ratios of 0, 20, 40, 60, and 100%. The selection for the mixture proportions for the various batches was based on the design of experiments (DOE) methodology. The hard density, compressive strength, splitting tensile strength, and flexural strength of concrete with a 100% replacement of granite with POC-aggregates reduced by 8.80, 37.25, 30.94, and 14.31%, respectively. Furthermore, a reduction in initial and ultimate torque was observed. While cracks increased with the increase in POC-aggregates. Finally, the cracking of concrete subjected to torsional loads was monitored and characterized by acoustic emissions (AE). The results illustrate a sudden rise in AE activities during the initiation of cracks and as the ultimate cracks were developed. This was accompanied by a sudden drop in the torque/twist curve.