The spin, or normalized angular momentum λ, of dark matter halos in cosmological simulations follows a log normal distribution and has little correlation with galaxy observables such as stellar masses or sizes. There is currently no way to infer the λ parameter of individual halos hosting observed galaxies. Here, we present a first attempt to measure λ starting from the dynamically distinct disks and stellar halos identified in high-resolution cosmological simulations with the Galactic Structure Finder (gsf). In a subsample of NIHAO galaxies analyzed with gsf, we find tight correlations between the total angular momentum of the dark matter halos, J
h, and the azimuthal angular momentum, J
z, of the dynamical distinct stellar components of the form: log(J
h) = α + β.log(J
z). The stellar halos have the tightest relation with α = 9.50 ±0.42 and β = 0.46 ±0.04. The other tight relation is with the disks, for which α = 6.15 ±0.92 and β = 0.68 ±0.07. While the angular momentum is difficult to estimate for stellar halos, there are various studies that calculated J
z for disks. In application to the observations, we used Gaia DR2 and APOGEE data to generate a combined kinematics-abundance space, where the Galaxy's thin and thick stellar disks stars can be neatly separated and their rotational velocity profiles, v
ph(R), can be computed. For both disks, v
ph(R) decreases with radius with ∼2 km/s/kpc for R ≥ 5 kpc, resulting in velocities of v
ph,thin = 221.2 ±0.8 km/s and v
ph,thick = 188 ±3.4 km/s at the solar radius. We use our derived v
ph,thin(R) and v
ph,thick(R) together with the mass model for the Galaxy of Cautun et al. (
2020MNRAS.494.4291C) to compute the angular momentum for the two disks: J_z, thin_ = (3.26 ±0.43)x10
13 and J_z, thick_ = (1.20 ±0.30)x10
13 M
☉.kpc.km/s, where the dark halo is assumed to follow a contracted NFW profile. Adopting the correlation found in simulations, the total angular momentum of the Galaxy's dark halo is estimated to be J
h=2.69
–0.32+0.37*10
15 M
☉.kpc.km/s and the spin estimate is λ
MW = 0.061
–0.016+0.022, which translates into a probability of 21% using the universal log normal distribution function of λ. If the Galaxy's dark halo is assumed to follow a NFW profile instead, the spin becomes λ
MW = 0.088
–0.020+0.024, making the Milky Way a more extreme outlier (with a probability of only 0.2%).