The present study evaluates the potential and suitability of different fractions of reclaimed asphalt pavement (RAP) for roller compacted concrete pavement (RCCP) mixes. Natural coarse and fine aggregates were replaced, partially and in combination, by coarse RAP, fine RAP, and combined RAP for preparation of RCCP mixes. The considered properties to determine the optimum RAP fraction and its proportion for RCCP were fresh density and water demand, compressive strength, flexural strength, split tensile strength, porosity, water absorption, abrasion resistance, and performance in aggressive environments of chloride- and sulfate-rich ions. It was observed that inclusions of all the fractions of RAP considered could reduce the strength related properties of RCCP mixes significantly at all curing ages. However, fine RAP mixes were found to exhibit better strength properties than coarse RAP and combined RAP mixes. It was also observed that none of the RAP mixes could achieve the recommended compressive strength criterion of 27.6 MPa, however, they exhibited enough flexural strength to replace a fraction of conventional aggregates, individually or in combination, for construction using RCCP. In fact, 50% coarse and 50% fine RAP mixes had higher flexural strength than the target laboratory mean strength of 4.3 MPa. Similarly, these mixes were found to have sufficient abrasion resistance and could be included in RCCP (surface course) to be constructed in areas having high concentrations of chloride and sulfate ions. Additionally, the results also indicated that higher proportions of fine RAP may be suggested for RCCP mixes to be laid in sulfatic environments.