QGIS has native support for this format. ESRI grid (.asc) files can be directly opened in QGIS by selecting Layers >>> Add Raster Layer. The .asc file can also be dragged and dropped into the QGIS session, rather than using the Add Raster Layer option.
But when I do either, I get this error: ".asc is not a supported raster data source". Same issue reported here. I'm using version 2.0.1-Dufour.