We present an analysis of archival HST/ACS imaging in the F475W ( g _ { 475 } ) , F606W ( V _ { 606 } ) and F814W ( I _ { 814 } ) bands of the globular cluster ( GC ) system of a large ( 3.4 kpc effective radius ) ultra-diffuse galaxy ( DF17 ) believed located in the Coma Cluster of galaxies . We detect 11 GCs down to the 5 \sigma completeness limit of the imaging ( I _ { 814 } =27 mag ) . Correcting for background and our detection limits yields a total population of GCs in this galaxy of 27 \pm 5 and a V -band specific frequency , S _ { N } = 28 \pm 5 . Based on comparisons to the GC systems of Local galaxies , we show that both the absolute number and the colors of the GC system of DF17 are consistent with the GC system of a dark-matter dominated dwarf galaxy with virial mass \sim 9.0 \times 10 ^ { 10 } M _ { \odot } and a dark-to-stellar mass ratio , M _ { vir } / M _ { star } \sim 1000 . Based on the stellar mass-growth of the Milky Way , we show that DF17 can not be understood as a failed Milky Way-like system , but is more similar to quenched Large Magellanic Cloud-like systems . We find that the mean color of GC population , g _ { 475 } – I _ { 814 } = 0.91 \pm 0.05 mag , coincides with the peak of the color distribution of intracluster GCs and are also similar to those of the blue GCs in the outer regions of massive galaxies . We suggest that both the intracluster GC population in Coma and the blue-peak in the GC populations of massive galaxies may be fed - at least in part - by the disrupted equivalents of systems such as DF17 .