  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. Assuming an absolute astrometric
precision floor for bright stars of 0.1 mas for the GBTDS, 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 to a PBH population at $f_{\rm
DM}$ down to $\approx10^{-1}-10^{-3}$ for $(10^{-1}-10^{2})M_{\odot}$ likely
yielding novel PBH constraints.
