  We prove that the generating functions for the colored HOMFLY-PT polynomials
of rational links are specializations of the generating functions of the
motivic Donaldson-Thomas invariants of appropriate quivers that we naturally
associate with these links. This shows that the conjectural links-quivers
correspondence of Kucharski-Reineke-Sto\v{s}i\'c-Su{\l}kowski as well as the
LMOV conjecture hold for rational links. Along the way, we extend the
links-quivers correspondence to tangles and, thus, explore elements of a skein
theory for motivic Donaldson-Thomas invariants.
