When the space shuttle crew gets in touch with its controllers at the Johnson Space Center in Houston, it uses a communications system designed by a unit of the Ford Motor Company. And the person who answers could well be a Ford employee.

''About half the guys in the control room are ours, the rest are with NASA,'' said Henry E. Hockeimer, president of the Ford Aerospace and Communications Corporation, in an interview before leaving to watch the launching at Cape Canaveral. ''We augment the Government people and you can't tell the difference when the system is operating.''

A spokesman for the National Aeronautics and Space Administration said that Pan American World Airways performs a similar function at the Kennedy Space Center in Florida. ''Basically, they provide an employee work force to carry out tasks not done by civil servants,'' he said. ''They can attract the needed technical people.''

Ford Aerospace has been the prime contractor for the Mission Control Center since 1963 and has 1,100 people working on the shuttle project. Because the shuttle, which is designed for a variety of tasks, is more complicated than earlier spacecraft, Mr. Hockeimer said the control center had to be completely redesigned with new computers and communications equipment. The conversion has taken more than two years and cost $47.6 million, NASA said.