How did the terms "acidic" and "basic" come to be associated with $SiO_2$ in igneous rocks?
The idea came from the theory that silicic acid was the chief form of silicon occurring in rocks.  Early attempts to classify minerals, placed some mineral specimens in groups based acid-base reactions and the hypothetical acid that mineral was derived.  Sulfates, phosphates, nitrates , and tungstates etc.  

This thinking was the result of 19th century chemistry research which attempted to explain chemical reactions in terms of  acid-base reactions.

Much of this terminology is still in use today even though it is considered archaic now.