Ultra-diffuse galaxies (UDGs) have the sizes of giants but the luminosities of dwarfs. A key to understanding their origins comes from their total masses, but their low surface brightnesses (μ (V) ≥slant 25.0) generally prohibit dynamical studies. Here, we report the first such measurements for a UDG (VCC 1287 in the Virgo cluster), based on its globular cluster system dynamics and size. From seven GCs we measure a mean systemic velocity vsys = {1071}-15+14 km s‑1, thereby confirming a Virgo cluster association. We measure a velocity dispersion of {33}-10+16 km s‑1 within 8.1 kpc, corresponding to an enclosed mass of (4.5 ± 2.8) × 109M⊙ and a g-band mass-to-light ratio of {({\text{}}M/L)}g={106}-54+126 within an effective radius. From the cumulative mass curve, along with the GC numbers, we estimate a virial mass of ∼8 × 1010M⊙, yielding a dark-to-stellar mass fraction of ∼3000. We show that this UDG is an outlier in Mstar–Mhalo relations, suggesting extreme stochasticity in relatively massive star-forming halos in clusters. Finally, we discuss how counting GCs offers an efficient route to determining virial masses for UDGs.