Scandrick was released Tuesday by the Redskins after signing a two-year deal with Washington this past offseason.
Washington coach Jay Gruden emphasized the move "had nothing to do with his play," saying the Redskins parted ways with Scandrick because of the unexpected emergence of their younger cornerbacks.
Scandrick, 31, spent his first nine seasons with the Dallas Cowboys. He appeared in 11 games for Dallas last season.
The Chiefs have been searching for veteran help at cornerback. They visited early in training camp with Bashaud Breeland but did not sign him.
Kansas City lost five of its top six cornerbacks from last season, including Marcus Peters. The Chiefs traded with Washington for Kendall Fuller and signed David Amerson as a free agent but are still thin in proven players at corner.
Information from ESPN's Adam Teicher was used in this report.