We prove that for any rationally connected threefold X, there exist a smooth projective surface S and a family of 1-cycles on X parameterized by S, inducing an Abel-Jacobi isomorphism \(\mathrm {Alb}(S)\cong J^3(X)\) . This statement was previously known for some classes of smooth Fano threefolds. We prove a similar result for the Walker Abel-Jacobi map on 1-cycles on higher-dimensional rationally connected manifolds.