Askew was a 2004 fellow at Civiella Ranieri in Umbertide, Italy, and a featured writer at the 2008 World Literature Today and Chinese Literature Conference in Beijing. In 2009, she received an Arts and Letters Award from the American Academy of Arts and Letters. Her essays and short fiction have appeared in Tin House, TriQuarterly, Nimrod, World Literature Today, and elsewhere. Her story "The Killing Blanket" was selected for Prize Stories 1993: The O. Henry Awards.
Askew's first novel The Mercy Seat (1997) was nominated for the PEN/Faulkner Award, the Dublin IMPAC Prize, was a Boston Globe Notable Book, and received the Oklahoma Book Award and the Western Heritage Award in 1998. In 2002, her second novel Fire in Beulah (2001), about the Tulsa race riot, received the American Book Award and the Myers Book Award from the Gustavus Myers Center for the Study of Bigotry and Human Rights. Askew's third novel, Harpsong (2007), is set in 1930's Oklahoma. Harpsong received the Oklahoma Book Award, the Western Heritage Award, the WILLA Award from Women Writing the West, and the Violet Crown Award from the Writers League of Texas in 2008. Her novel about state immigration laws, "Kind of Kin," was published by Ecco in 2013.