Given a surface S, and a group G, one can construct a variety (called a character variety) which parametrizes all representation from $\pi_{1}(S)$ to G up to conjugacy. The mapping class group of S acts on these varieties, an action whose dynamics of this action have been the subject of much study. For a given mapping class, and and a wide collection of character varieties, we compute an invariant called algebraic entropy which gives a measure of the complexity of the action which has an algebraic flavor.