First, were you still working for that California company after you moved to South Carolina? If you were - and if you did not move to SC at the company's request - then you likely owe tax to California for the whole year anyway.
If it turns out that you don't owe CA tax because you were working for a new company, then your first employer has already sent all the withholding to the state of California. The only way to "get it back" is to file both state tax returns. Do the California return first, then the SC one. The income tax that you pay to California will appear as a credit on your SC return. This is how most states handle double taxation.
This credit will appear on line 1 of form SC1040TC.
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