She grew up in Chappaqua, New York, and studied at Barnard College and New York University. Swenson has been Poet-in-Residence at Skidmore College, the University of Idaho, University of Denver, Clark University, Scripps College and Barnard College. She taught at City College, New York. Her work has appeared in The New York Times, The Beloit Poetry Journal, Paris Review, American Poetry Review, "Saturday Review", and "The New Yorker".