  Let $X$ be a complex projective surface with arbitrary singularities. We
construct a generalized Abel--Jacobi map $A_0(X)\to J^2(X)$ and show that it is
an isomorphism on torsion subgroups. Here $A_0(X)$ is the appropriate Chow
group of smooth 0-cycles of degree 0 on $X$, and $J^2(X)$ is the intermediate
Jacobian associated with the mixed Hodge structure on $H^3(X)$. Our result
generalizes a theorem of Roitman for smooth surfaces: if $X$ is smooth then the
torsion in the usual Chow group $A_0(X)$ is isomorphic to the torsion in the
usual Albanese variety $J^2(X)\cong Alb(X)$ by the classical Abel-Jacobi map.
