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Alpha Ophiuchi (Rasalhague) is a nearby rapidly rotating A5IV star that has been imaged by infrared interferometry. α Oph is also part of a known binary system, with a companion semimajor axis of ∼430 mas and a high eccentricity of 0.92. The binary companion provides the unique opportunity to measure the dynamical mass to compare with the results of rapid rotator evolution models. The lack of data near periastron passage limited the precision of mass measurements in previous work. We add new interferometric data from the MIRC combiner at the CHARA Array as well as new Keck adaptive optics imaging data with NIRC2, including epochs taken near periastron passage. We also obtained new radial velocities of both components at Fairborn Observatory. Our updated combined orbit for the system drastically reduces the errors of the orbital elements and allows for precise measurement of the primary star mass at the few percent level. Our resulting primary star mass of 2.20 ± 0.06 M⊙ agrees well with predictions from imaging results and matches evolution models with rotation when plotting on a Hertzsprung–Russell diagram. However, to truly distinguish between nonrotating and rotating evolution models for this system, we need ∼1% errors on mass, which might be achieved once the distance is known to higher precision in future Gaia releases. We find that the secondary mass of 0.824 ± 0.023 M⊙ is slightly underluminous when compared to stellar evolution models. We show that α Oph is a useful reference source for programs that need ±1 mas astrometry.