Is it possible to share folders to an individual user in ArcGIS Online?

No, it is not possible to share folders with an individual user in ArcGIS Online. As a workaround, create a group, add the user, and share the items from the folder with the group. To do so, follow the instructions described below.

Note:
The following actions require administrative privileges for groups created with update capabilities. Refer to ArcGIS Online: Administrative privileges for more information.

1. In ArcGIS Online, create a group, and add the required user to the group.
2. Navigate to the desired folder and share items in the folder to the group.

The following image shows the Share icon on the Contents tab in ArcGIS Online.