Taking off at about 19:21 local time (02:21 GMT), the first stage of the rocket returned safely to the air base about eight minutes later.
Californians posted videos and photos of the skies after the successful take-off, including Los Angeles mayor Eric Garcetti.
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SpaceX has developed reusable rockets in a bid to save costs and attract business.
While the company says this is the 30th landing of a booster, this is the first land touchdown on the West Coast - the rest have happened on land in Florida and from platforms out at sea.
Argentina's satellite will reportedly track natural disasters, crop yields and soil-moisture levels from 385 miles (620km) above the earth.
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