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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 $\propto$ age$^{-1/2}$, requires the current solar angular momentum-loss rate to be around $6\times 10^{30}$erg. Magnetohydrodynamic models, and previous observations of the solar wind (from the Helios and Wind spacecraft), generally predict a values closer to $1\times 10^{30}$erg or $3\times 10^{30}$erg, respectively. Recently, the Parker Solar Probe (PSP) observed tangential solar wind speeds as high as $\sim50$km/s in a localized region of the inner heliosphere. If such rotational flows were prevalent throughout the corona, it would imply that the solar wind angular momentum-loss rate is an order of magnitude larger than all of those previous estimations. In this letter, we evaluate the angular momentum 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 angular momentum fluxes. We analyse two solar wind streams that were repeatedly traversed by PSP; the first is a slow wind stream whose average angular momentum flux fluctuates between positive to negative, and the second is an intermediate speed stream containing a positive angular momentum flux (more consistent with a constant flow of angular momentum). When the data from PSP is evaluated holistically, the average equatorial angular momentum flux implies a global angular momentum-loss rate of around $2.6-4.2\times 10^{30}$ erg (which is more consistent with observations from previous spacecraft).