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You probably can, at least in principle. The SAT is effectively an IQ test (it correlates as well with IQ tests as they correlate with each other) and you can definitely study for that. The difference is that there aren't Stanford-Binet prep classes (at least I don't think so.)

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SAT scores and IQ may be correlated, but the fact you can study for the SAT means that it's a weak indicator of 'natural' intelligence.

My friend scored 70 points higher than me on the math section and yet he was totally lost in calculus II and eventually dropped the class (while I consistently scored the highest on tests). His strategy was to try and memorize the answers/procedures rather than understand the principles behind them (which is the name of the game in prepping for the SAT).

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