"Heâs (Graham) had some success in this league, and I think the competition will be good for them," coach Gary Kubiak said. "I want to see them compete because it should bring out the best in them."
The Texans drafted Bullock in the fifth round out of Texas A&M.
Graham has kicked for seven teams since entering the league in 2001, most notably the Cincinnati Bengals from 2003-09. He appeared briefly for both the Miami Dolphins and the Baltimore Ravens in 2011.