The 38-year-old slugger, fifth on baseball's home-run list, got to the complex several hours before the Rangers' first full-squad workout.
Sosa has a minor league deal with his original team, hoping for a chance to get back to the major leagues.
On his way to the practice field, Sosa passed through a small group of fans, with one yelling, "Good luck, Sammy." He stopped and posed for a picture.
"I just expect Sammy to come in and be Sammy," first-year manager Ron Washington said. "We're going to do everything we can to try to get him going and maybe he can help us win some ballgames."
Wearing a short-sleeve shirt with yellow and light blue stripes when he first arrived around dawn, Sosa joked with reporters by looking at his watch as if to remind them he showed up early.
Sosa completed his physical and greeted teammates in the clubhouse. With a bat in hand, he smiled and said, "Back in business." The Rangers planned an afternoon news conference for the former NL MVP and seven-time All-Star who has 588 homers.
Rangers owner Tom Hicks, who was in camp for Sosa's first day, said he's anxious to see how things are going for Sosa after a few weeks in camp.
"He says all the right things," Hicks said. "He just has to go out and do it now. I think he will."
Sosa was 16 when Texas signed him from the Dominican Republic in 1985. He was still a lanky kid in 1989 when he made his major league debut and hit his first home run, the only one he had in 25 games for the Rangers before being traded to the Chicago White Sox.
When Sosa's minor league deal with Texas was announced last month, Sosa was fielding the same steroids questions that dogged him when he left the game after the 2005 season with Baltimore.
Before his season with the Orioles, when he hit .221 with 14 home runs and 45 RBIs in 102 games, Sosa was one of several players who testified before a congressional committee looking into steroid use in professional baseball.
Like Mark McGwire, Sosa is suspected by some of having used steroids before they were banned by baseball after the 2002 season. Sosa said last month his comeback isn't about disproving the rumors that performance-enhancing drugs elevated him among the game's most feared power hitters.
If Sosa makes the team, Washington expects him to be primarily a designated hitter and bat in the middle of the lineup behind three-time All-Star shortstop Michael Young and switch-hitting slugger Mark Teixeira.
Sosa will get a $500,000, one-year deal and could possibly earn up to $2.1 million more in performance bonuses if he makes the 40-man roster.
"We're excited to see what he can bring," Teixeira said.
In his career, Sosa has batted .274 with 1,575 RBIs with three 60-homer seasons.
"Obviously, taking a year off, it's tough to predict what he's going to be able to do," Young said. "The great thing about him is that he has that burning desire to go out and succeed. He's a proud guy. He's not going to go out here and just play to be average."
Sosa's MVP season was in 1998, when he batted .308 with a career-high 66 homers and 158 RBIs for the Chicago Cubs. That year he was in the home run chase with McGwire, who became the first major leaguer to hit 70 homers.