Basalt fiber–reinforced polymer (BFRP) has been the most recent fiber–reinforced polymer (FRP) composite material introduced as reinforcement and prestressing tendons for concrete. Measuring the mechanical properties of BFRP rod/tendon is challenging using the existing mechanical testing methods due to their relatively lower transverse direction strength. Hence, gripping of the BFRP rods using the conventional wedge-type anchors becomes unsuitable because it causes stress concentration and exerts localized high transverse pressure on the specimen, which results in premature failure at the grips, instead of the desired rupture of the gauge section. This study is focused on the development of a new anchor for the prestressing of the BFRP rods based on using expansive cement as a grout material. The goal is to ensure a uniform distribution of pressure around the BFRP rods to avoid their failure within the wedge during prestressing. Pull-out tests were conducted on several samples with different anchor dimensions to study the interaction between the expansive cement and the BFRP rod. The parameters affecting the gripping behavior were investigated, and the design of the anchor was optimized based on finite-element simulations using commercially available software.