This is relevant to a little question in quantum computation. I even asked Serre. He didn't know. Before you buy. In fact the existence of a low-dimensional faithful representation is a strong condition.
Free groups are very special.
In particular, it cannot be faithful. That is a more reasonable question, but the answer is still negative. But there are finitely presentable groups which are not residually finite and therefore can not have a faithful representation. The first such example is due to Higman, I believe.