The team is also placing WR Cody Hollister on injured reserve.
Basham, 28, is a former third-round pick of the Colts back in 2017. He was waived a year later and claimed off waivers by the Jets and played out his four-year, $3.35 million contract.
He signed a two-year, $6.5 million deal with the Cowboys in 2021 and is in the final year of his contract. Dallas elected to waive him last week.
In 2022, Basham has appeared in two games for the Cowboys and recorded no statistics.