A source told local news website San Angelo LIVE the derrick hand, Roy Michael Jaynes, was tripping pipe out for logging before the accident.
"He was about 50-55 feet (about 16-19 metres) up on the derrick itself and almost done," the source reportedly said.
"He fell and hit the rig floor."
Jaynes was apparently new to working on the derrick and it is not known if he was wearing a safety harness at the time.
The accident occurred at Turner Ranch in the northwest of Tom Green County, with the rig believed to be owned by Heartland Drilling.
"This was a sad, sad accident," local Sheriff David Jones reportedly said.
"We haven't had a drilling accident death in the county in years."