Yes, there were a whole bunch of studies all of which point to education level as having very high predictive power (with positive correlation) as far as voter turnout, probably the highest exogenous predictive factor they found. I won't list all the studies, but will point to a paper that DOES list a bunch of them: "The Dynamic Effects of Education on Voter Turnout" (2009) by Barry C. Burden if University of Wisconsin.
As a side note, if you want to find tons of studies on the topic, google for the ones that cite Brody's paper discussed below.
As a side note, in American politics, there is a very interesting conundrum, which leads to your question's answer to both "yes" and "no", called "Brody's puzzle".
It's named after a research by Brody in 1978 [Brody, R.A. (1978) "The puzzle of political participation in America"], which found that while education predicts
whether individuals will vote, over time rising levels of education did not increase aggregate turnout. The paper linked above tries to research the topic.