The cement mortar mixes were developed with the intent of testing the suitability of fine graded reclaimed asphalt pavement aggregates as a replacement for naturally fine materials. The natural fine aggregates were replaced in multiple percent levels of 25%, 50%, 75%, and 100% by weight. The results demonstrate that the mechanical qualities of the mortar mix are deteriorating. To address this, zinc industry waste - jarosite was used as a part replacement for cement in proportions of 5%, 10%, and 15%. Jarosite improved the microstructural, mechanical, and shrinkage properties. For instance, when comparing with the control mix, the mix containing 25% fine reclaimed asphalt pavement aggregates shows a reduction of 5.5% in hardened density and 14% in compressive strength. On the other hand, when 10% jarosite is included in the 25% fine reclaimed asphalt pavement mix, there is an observed increase of 4.85% in hardened density and 7% in compressive strength with respect to the mix containing 25% fine reclaimed asphalt pavement aggregates. As a result, the current study proposes using 10% jarosite when fine reclaimed asphalt pavement aggregates are used to make cement mortar mixes. Furthermore, a cost analysis is performed to determine the difference in construction costs. These findings are expected to inspire rational mix design recommendations for mortar mixes including fine reclaimed asphalt pavement aggregates, as well as bring environmental and economic benefits by lowering carbon footprints.