  Vector leptoquarks can address the lepton flavor universality anomalies in
decays associated with the $b \to c \ell \nu$ and $b \to s \ell \ell$
transitions, as observed in recent years. Generically, these leptoquarks yield
new sources of CP violation. In this paper, we explore constraints and
discovery potential for electric dipole moments (EDMs) in leptonic and hadronic
systems. We provide the most generic expressions for dipole moments induced by
vector leptoquarks at one loop. We find that $O(1)$ CP-violating phases in tau
and muon couplings can lead to corresponding EDMs within reach of
next-generation EDM experiments, and that existing bounds on the electron EDM
already put stringent constraints on CP-violating electron couplings.
