  We compute the $p$-primary components of the linking pairings of orientable
3-manifolds admitting a fixed-point free $S^1$-action. Using this, we show that
any non-singular linking pairing on a finite abelian group with homogeneous
2-primary summand is realized by such a manifold. However, some pairings on
inhomogeneous 2-groups are not realizable by any Seifert fibred 3-manifold.
