The long-term evolution of the Sun's rotation period cannot be directly observed, and is instead inferred from trends in the measured rotation periods of other Sun-like stars. Assuming the Sun spins down as it ages, following rotation rate ∝ age−1/2, requires the current solar angular momentum (AM) loss rate to be around 6 × 1030 erg. Magnetohydrodynamic models, and previous observations of the solar wind (from the Helios and Wind spacecraft), generally predict a values closer to 1 × 1030 erg or 3 × 1030 erg, respectively. Recently, the Parker Solar Probe (PSP) observed tangential solar wind speeds as high as ~50 km s−1 in a localized region of the inner heliosphere. If such rotational flows were prevalent throughout the corona, it would imply that the solar wind AM-loss rate is an order of magnitude larger than all of those previous estimations. In this Letter, we evaluate the AM flux in the solar wind, using data from the first two orbits of PSP. The solar wind is observed to contain both large positive (as seen during perihelion), and negative AM fluxes. We analyze two solar wind streams that were repeatedly traversed by PSP; the first is a slow wind stream whose average AM flux fluctuates between positive and negative values, and the second is an intermediate speed stream that contains a positive AM flux (more consistent with a constant flow of AM). When the data from PSP are evaluated holistically, the average equatorial AM flux implies a global AM-loss rate of around (2.6–4.2) × 1030 erg (which is more consistent with observations from previous spacecraft)