  We study spin density wave quantum critical points in two dimensional metals
with a quenched disorder potential coupling to the electron density. Adopting
an $\epsilon$-expansion around three spatial dimensions, where both disorder
and the Yukawa-type interaction between electrons and bosonic order parameter
fluctuations are marginal, we present a perturbative, one-loop renormalization
group analysis of this problem, where the interplay between fermionic and
bosonic excitations is fully incorporated. Considering two different Gaussian
disorder models restricted to small-angle scattering, we show that the
non-Fermi liquid fixed point of the clean SDW hot-spot model is generically
unstable and the theory flows to strong coupling due to a mutual enhancement of
interactions and disorder. We study properties of the asymptotic flow towards
strong coupling, where our perturbative approach eventually breaks down. Our
results indicate that disorder dominates at low energies, suggesting that the
ground-state in two dimensions is Anderson-localized.
