The Civil War was certainly a watershed moment in United States history, and one could make the point that it was revolutionary from a number of perspectives.
Perhaps the most important issue (and where the Civil War was at its most revolutionary) applied to slavery. Before the Civil War, the Southern states were slave-owning societies and, with the Emancipation Proclamation, the Civil War became (from a Northern Perspective) a struggle to bring an end to this slave-holding culture. With the defeat of the Southern States, slavery was quickly ended with the passing of the Thirteenth Amendment. Later amendments passed during reconstruction would extend citizenship and voting rights. This was a revolutionary and critical step forward for American democracy.
In addition, we could discuss the issue of secession. Attempting secession was a radical step by the Southern states. It was also the most extreme expression of States's Rights theory (and States's Rights has had a long history in U.S. political thought). In stating that the states had the legal right to secede and acting upon that statement, the Southern states were presenting a challenge to the United States's very identity as a nation. In defeating the South and bringing it back into the Union, the United States disarmed an ideological challenge that could have had unimaginable implications for the future.
Finally, there were a number of additional factors that would qualify as turning points for US military history themselves. This was the first conflict in which the U.S. government adopted conscription (and both the North and the South instituted their own drafts). In addition, there was the introduction of breech-loaded rifles, which vastly improved range and accuracy, resulting in the vast and devastating casualties we associate with the Civil War experience.
In conclusion, there are a lot of issues that can be discussed in this question, and a lot of perspectives from which we can call the Civil War revolutionary, and a turning point in US history.