Hello - Yes, you can do this out of the box. When you publish from ArcMap, follow the directions for that environment. This will create either a hosted feature service or a map image layer depending upon the settings you select during publishing. This item will be only viewable to you initially unless you share more broadly during publishing. Next you will move to ArcGIS Online to create a webmap.
Web maps—ArcGIS Online Help | ArcGIS
Once you have the web map, you can share it directly or build an application around it (Web AppBuilder or Template Applications).
Adam Z