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Abstract 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_DM) in the (10⁻⁹–10)M_⊙mass ranges come from photometric microlensing and boundf_DM≲ 10⁻²–10⁻¹. With the advent of the Roman Space Telescope with its submilliarcsecond 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 contain different information, making it a complimentary lensing probe. At submilliarcsecond 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 ≈10³f_DMfor a population of 1M_⊙PBHs and tapers to ≈10f_DMand ≈100f_DMat 10⁻⁴M_⊙and 10³M_⊙, respectively. Accounting for the distinguishability of PBHs from stellar lenses, we conclude the GBTDS will be sensitive to a PBH population atf_DMdown to ≈10⁻¹–10⁻³for (10⁻¹–10²)M_⊙likely yielding novel PBH constraints.