Primordial Black Holes (PBHs) could explain some fraction of dark matter and shed light on many areas of early-universe physics. Despite over half a century of research interest, a PBH population has so far eluded detection. The most competitive constraints on the fraction of dark matter comprised of PBHs ($f_{\rm DM}$) in the $(10^{-9}-10)M_{\odot}$ mass-ranges come from photometric microlensing and bound $f_{\rm DM}\lesssim10^{-2}-10^{-1}$. With the advent of the Roman Space Telescope with its sub-milliarcsecond (mas) astrometric capabilities and its planned Galactic Bulge Time Domain Survey (GBTDS), detecting astrometric microlensing signatures will become routine. Compared with photometric microlensing, astrometric microlensing signals are sensitive to different lens masses-distance configurations and contains different information, making it a complimentary lensing probe. At sub-mas astrometric precision, astrometric microlensing signals are typically detectable at larger lens-source separations than photometric signals, suggesting a microlensing detection channel of pure astrometric events. We use a Galactic simulation to predict the number of detectable microlensing events during the GBTDS via this pure astrometric microlensing channel. We find that the number of detectable events peaks at $\approx 10^{3} f_{\rm DM}$ for a population of $ 1 M_{\odot}$ PBHs and tapers to $\approx 10f_{\rm DM}$ and $\approx 100f_{\rm DM}$ at $10^{-4}M_{\odot}$ and $10^{3}M_{\odot}$, respectively. Accounting for the distinguishability of PBHs from Stellar lenses, we conclude the GBTDS will be sensitive and PBH population at $f_{\rm DM}$ down to $\approx10^{-1}-10^{-3}$ for $(10^{-1}-10^{2})M_{\odot}$ likely yielding novel PBH constraints.