Zawacki's first book, By Reason of Breakings, won the 2001 University of Georgia Contemporary Poetry Series, chosen by Forrest Gander.
He has held fellowships from the Collège International des Traducteurs Littéraires and the Résidence internationale Ville de Paris / Institut Français aux Récollets in France, the Bogliasco Foundation] in Italy, Hawthornden Castle in Scotland, Le Château de Lavigny in Switzerland, the Salzburg Seminar in American Studies in Austria, the University of Paris IV—La Sorbonne in France, the Slovenian Writers' Association in Slovenia, the Millay Colony, the Saltonstall Colony, and the Bread Loaf Writers' Conference.
He is also the translator, from the French, of poet and psychoanalyst Sébastien Smirou's books See About: Bestiary (La Presse / Fence (magazine), 2017) and My Lorenzo, published in 2012 by Burning Deck with an introduction by Jennifer Moxley.
The French edition of Zawacki's first book, Par Raison de brisants, translated by Antoine Cazé, was issued by Éditions Grèges in 2011 and was a finalist for Le Prix Nelly Sachs.
Translated by Anne Portugal, Sonnetssonnants appeared in a bilingual edition in the Collection américaine from Joca Seria.