The 34-year-old missed last season after surgery to repair a torn flexor tendon in his right arm. He would get a $750,000, one-year contract if added to the 40-man roster.
Astros general manager Ed Wade said that scout Jack Lind saw Ortiz work out in September "and was pleased with what he saw."
"By all accounts, Russ has rebounded well from Tommy John surgery, and we have no doubt that a healthy Russ Ortiz should be able to come to camp and be a serious contender for a spot in the big league rotation," Wade said. "He'll have every opportunity in spring training to win a job."
Ortiz is 110-82 with a 4.42 ERA in 282 career games, including 253 starts. He's played for San Francisco (1998-2002, 2007), Atlanta (2003-04), Arizona (2005-06) and Baltimore (2006).
Ortiz led the NL with 21 wins in 2003 and was selected for the All-Star team.