Robert E. Lee: Civil War General is a computer wargame with turn-based gameplay, which unfolds on a hex map playing field. Set during the American Civil War, the game casts players in the role of General Robert E. Lee, and tasks them with leading the Confederate Army of Northern Virginia to victory over the Union Army of the Potomac. It portrays eight Civil War conflicts, including the Battle of Gettysburg, the Battle of the Wilderness and a speculative scenario in which Lee lays siege to Washington, D.C.

I'm not sure if it was that game I played as a kid, or the sequel.