No. Sweet apple cider sold in the U.S. has no alcohol, because Americans use the word cider for unfermented, usually unfiltered apple juice; only hard cider, which is fermented, contains alcohol.
The names flip in many other countries, particularly in Europe, where cider means the fermented drink and the unfermented product is simply called apple juice. Hard cider is made much like wine: the fruit is crushed and pressed, and yeast ferments the juice, converting its sugar into alcohol. Because apples naturally contain 10% to 20% sugar, hard ciders usually finish at 4% to 9% alcohol by volume (ABV). In most states, cider must stay below 7% ABV or it is taxed at a higher rate similar to wine, although some states, such as Virginia, allow ciders up to 10% ABV. Adding sugar to the juice before fermentation produces a stronger drink often called apple wine, and freeze-concentrating hard cider makes applejack, which is stronger still.
Source: Apples Extension (eXtension, USDA NIFA-supported), An Introduction to Hard Cider in the U.S.
Image: Cider apple press, Hereford, by Brian Deegan, CC BY-SA 2.0, via Wikimedia Commons.