Jack Jamisson Kinsler joined the family Wednesday afternoon, weighing 6 pounds, 9 ounces. Davis was in Wednesday's lineup at third base, batting ninth against the Tigers.
Kinsler is the second Rangers player to take advantage of the new paternity leave rule Major League Baseball instituted this year. The rule allows players to leave their teams for 24 to 72 hours due to the birth of their children. Pitcher Colby Lewis was the first MLB player to exercise that option when his daughter was born in April.
"We have a fertile club," general manager Jon Daniels joked.
Kinsler is expected to return to the team on Friday, manager Ron Washington said.