No. The San Andreas Fault System, which crosses California from the Salton Sea in the south to Cape Mendocino in the north, is the boundary between two tectonic plates — the Pacific Plate and North American Plate. The Pacific Plate is moving northwest with respect to the North American Plate at approximately 46 millimeters per year (about the rate your fingernails grow). The strike-slip earthquakes on the San Andreas Fault are a result of this plate motion. The plates are moving horizontally past one another, so California is not going to fall into the ocean. However, in about 12 million years, Los Angeles and San Francisco will be adjacent to one another!

Contributing source: USGS