SANTA BARBARA, Calif. (AP) _ A member of the Secret Service detail guarding President Reagan at his mountaintop ranch was injured Wednesday when the agent's jeep overturned, a White House spokesman said.

Deputy Press Secretary Peter Roussel identified the agent as George Lee. Lee suffered head injuries, but they were not serious, Roussel said.

''He was riding in the jeep and it hit a rock and overturned,'' the spokesman said, adding that Lee ''was out on post'' guarding the area.

Much of the president's land in the Santa Ynez Mountains is marked by rough terrain.

Lee was taken by ambulance from the remote mountaintop ranch to Santa Barbara's Cottage Hospital, Roussel said.

He said the incident took place in the early afternoon, prior to the time that Vice President George Bush and his wife Barbara visited the Reagans at their small adobe ranch house.

Bush and his wife spent an hour with the Reagans after the vice president participated in a celebration of V-J Day in San Francisco.