We present XRISM Resolve observations of the core of the hot, relaxed galaxy cluster Abell 2029 (A2029). We find that the line-of-sight bulk velocity of the intracluster medium (ICM) within the central 180 kpc is at rest with respect to the brightest cluster galaxy, with a 3 σ upper limit of ∣ v _bulk ∣ < 100 km s ⁻¹ . We robustly measure the field-integrated ICM velocity dispersion to be σ _v = 169 ± 10 km s ⁻¹ , obtaining similar results for both single-temperature and two-temperature plasma models to account for the cluster cool core. This result, if ascribed to isotropic turbulence, implies a subsonic ICM with Mach number M 3 D ≈ 0.22 and a nonthermal pressure fraction of 2.6 ± 0.3%. The turbulent velocity is similar to what was measured in the core of the Perseus cluster by Hitomi, but here in a more massive cluster with an ICM temperature of 7 keV, the limit on the nonthermal pressure fraction is even more stringent. Our result is consistent with expectations from simulations of relaxed clusters, but it is on the low end of the predicted distribution, indicating that A2029 is an exceptionally relaxed cluster with no significant impacts from either a recent minor merger or active galactic nucleus activity.