The 41-year-old Garcia had individual workouts in Houston following injuries to both Matt Schaub and Matt Leinart. Houston signed Delhomme last week to back up Yates, who completed 12 of 25 passes for 188 yards and a touchdown in a 17-10 win over Atlanta.
Houston (9-3) plays at Cincinnati (7-5) on Sunday, and can clinch the AFC South with a victory and a Tennessee loss.
The Texans also signed punter Matt Turk, who played for them from 2007-10. The 43-year-old Turk replaces Brett Hartmann, who was placed on injured reserve after tearing a left knee ligament Sunday. Turk was cut by Jacksonville in October.